Hydraulic systems serve as the primary drive mechanism for deep-sea submersibles. As these vehicles descend, ambient pressure increases from 0 to 110 MPa, inducing elastic deformation in the spool and sleeve that alters damping forces and compromises flow stability. To address this challenge, we propose a segmentation calculation method (SCM) that efficiently captures the dual nonlinear coupling between pressure distribution and cross-sectional geometry in predicting radial deformation. The SCM eliminates the need for iterative Multiphysics simulations by integrating analytical fluid-structure interaction into a single modeling process, reducing computational cost while maintaining high fidelity. Validation against three-dimensional finite element analysis (FEA) shows strong agreement, with a coefficient of determination (R2 = .87) across 441 evaluation points-corresponding to an 89.6% variance explained in radial deformation. Although experimental validation is not yet available, consistency with both FEA and computational fluid dynamics (CFD) results supports the model's reliability. Using the SCM, we further compare damping characteristics for spool-sleeve pairs made of steel, alumina, and silicon nitride, offering practical insights for the design of full-ocean-depth hydraulic valves.
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