Nonlinear sealing force of a seawater balance valve used in an 11000-meter manned submersible

Abstract

Balance valve is a core component of the 11000-meter manned submersible “struggle,” and its sealing performance is crucial and challenging when the maximum pressure difference is 118 MPa. The increasing sealing force improves the sealing performance and increases the system’s energy consumption at the same time. A hybrid analytical–numerical–experimental (ANE) model is proposed to obtain the minimum sealing force, ensuring no leakage at the valve port and reducing energy consumption as much as possible. The effects of roundness error, environmental pressure, and materials on the minimum sealing force are considered in the ANE model. The basic form of minimum sealing force equations is established, and the remaining unknown coefficients of the equations are obtained by the finite element method (FEM). The accuracy of the equation is evaluated by comparing the independent FEM data to the equation data. Results of the comparison show good agreement, and the difference between the independent FEM data and equation data is within 3% when the environmental pressure is 0–118 MPa. Finally, the minimum sealing force equation is applied in a balance valve to be experimented using a deep-sea simulation device. The balance valve designed through the minimum sealing force equation is leak-free in the experiment. Thus, the minimum sealing force equation is suitable for the ultrahigh pressure balance valve and has guiding significance for evaluating the sealing performance of ultrahigh pressure balance valves.

Key words： seawater balance valve; sealing performance; hybrid ANE model; FEM; minimum sealing force equation

Nomenclature

Abbreviations
ANE	Analytical–numerical–experimental
FEM	Finite element method
SHVBS	Seawater hydraulic variable ballast system
Variables
a	Half of contact width between the ball and the valve seat
C1	A correction factor
C2, C3	Unknown coefficients used to account for the simplification of the model
d	Inlet diameter
db	Diameter of the ball
D	Push rod diameter
E	Young’s modulus of the ball or valve seat
E*	Equivalent elastic modulus of the ball and valve seat
E1, E2	Elastic moduli of the ball and the valve seat, respectively
Eb, Ec	Elastic modulus of the bearing and the cylinder, respectively
Er	Relative error
F	Sealing force between the ball and the valve seat
Fh	Hydraulic force caused by the area difference between the push rod and the inlet
Fh1, Fh2	Hydraulic forces generated by the push rod area and the inlet area, respectively
Fmin	Minimum sealing force between the ball and the valve seat
Fs	Spring force
G	Shear modulus of the ball or valve seat
IT	Machining accuracy of the valve seat
K	Bulk modulus of the ball or valve seat
l	Length of the cylinder in the contact zone
p	Setting pressure inside the deep-sea simulation device
pe	Environmental pressure
P	Normal load on the valve seat
Q	Rated flow of the balance valve
r	Contact circle between the ball and the valve seat
R	Radius of the ball
x	Position at the contact zone
δ	Radial deformation of the valve seat
Δ	Roundness error of the valve seat
ν1, ν2	Poisson’s ratios of the ball and the valve seat, respectively
νb, νc	Poisson’s ratios of the bearing and the cylinder, respectively
σ	Total contact stress between the ball and the valve seat
σ1	Compensated contact stress generated by the spring force
σ2	Net contact stress
σmax	Maximum contact stress between the ball and the valve seat
σs	Tensile yield strength of the ball or valve seat
σsc	Compressive yield strength of the ball or valve seat
θ	Half cone angle of the valve seat
γ	Structural parameters of the bearing
ρ	Density of the ball or valve seat
ξ	Functional relationship between roundness error and spring force

Acknowledgements

The authors would like to thank the National Natural Science Foundation of China (Grant Nos. 52122502, 51879114, and 52075192).

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