⚡ electrical engineering

Sealing performance of particle-adhered rough interfaces: Reconstruction of equivalent rough surfaces and contact-mechanics analysis

This study establishes a particle-adhered equivalent rough-surface reconstruction model and a 3D finite-element contact analysis to demonstrate that particle size, rather than coverage, is the dominant factor intensifying stress concentrations and degrading the sealing performance of interfaces in particle-laden environments.

Original authors: Haitao Zheng, Jialiang Wang, Bo Li, Lubo Tang, Yongzheng Jang, Buyan Wan

Published 2026-10-06

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CC BY 4.0

Original authors: Haitao Zheng, Jialiang Wang, Bo Li, Lubo Tang, Yongzheng Jang, Buyan Wan

Original paper licensed under CC BY 4.0 (https://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

In the deep ocean, where the pressure is crushing and the water is thick with mud and rock fragments, engineers face a silent enemy: tiny solid particles. When machines drill for energy or explore the seabed, they rely on seals to keep high-pressure fluids contained. These seals are not perfectly smooth; like all metal surfaces, they are covered in microscopic hills and valleys. When solid particles, such as rock dust or sand, get trapped between a seal and the metal it presses against, they can ruin the seal's ability to hold back pressure. The problem is not just that the particles scratch the surface; it is that they change how the two surfaces touch. Instead of pressing together evenly, the load becomes uneven, creating weak spots where leaks can start. Understanding exactly how these tiny intruders alter the contact between rough surfaces is critical for keeping deep-sea drilling equipment safe and functional.

A team of researchers from the Sanya Institute of Hunan University of Science and Technology has developed a new way to visualize and measure this hidden interaction. They focused on a specific scenario common in deep-sea drilling: a pressure-retaining cap that seals a core barrel to keep samples intact. In this environment, rock cuttings suspended in seawater can become trapped inside the sealing mechanism. To study what happens next, the scientists created a digital model of a rough metal surface, similar to the one found on a drilling tool, and then simulated the random attachment of solid particles onto it. They did not simply add bumps to a flat sheet; they built a complex, three-dimensional representation of the actual rough terrain, complete with its natural peaks and valleys, and then carefully mapped how particles of different sizes would settle into those specific locations. This allowed them to reconstruct an "equivalent" surface that looked like the original rough metal but included the subtle, localized changes caused by the stuck particles.

Using this reconstructed surface, the researchers ran detailed computer simulations to see how a rubber-like seal ring would behave when pressed against it. They tested a wide range of conditions, varying the size of the trapped particles, and changing how many particles covered the surface from 10 percent to 50 percent. The goal was to see how these variables changed the pressure distribution, the total force the seal could hold, and the actual area where the two surfaces touched. The simulations revealed that the original shape of the metal surface was the most important factor in deciding where the highest stresses would occur. The highest pressure points always stayed near the tallest peaks of the original rough surface, regardless of the particles. However, the particles acted like amplifiers. When a particle landed on one of these high peaks, it intensified the stress in that specific spot, making the load distribution across the seal much more uneven than it would be on a clean surface.

The study found that the size of the particle mattered far more than how many of them were present. When the particles were very small, their effect was minimal. Even with a high number of them covering the surface, the seal's ability to hold pressure and the area of contact changed by less than 5 percent. But as the particles grew larger, the situation changed dramatically. When the particle size reached a medium level, the total force the seal could withstand increased by roughly 8 to 14 percent, and the actual contact area grew by about 9 percent. When the particles were as large as possible, the changes became even more significant, with the contact force and average pressure rising by 15 to 25 percent. This happened because larger particles created more substantial local bumps, forcing the seal to press harder against fewer, higher points on the metal surface. This concentration of force created a more dangerous, uneven stress pattern that could compromise the seal's integrity.

Interestingly, the number of particles, or the coverage, did not always make the problem worse in a straight line. Sometimes, having more particles actually reduced the overall deviation from the ideal state, depending on exactly where they landed relative to the metal's natural peaks. The researchers introduced a "safety margin" score to measure how far the contact state had drifted from a clean surface. For the smallest particles, this score remained very low, indicating a stable seal. For the medium-sized particles, the score rose as coverage increased, reaching a deviation of about 0.09. The most dramatic shifts occurred with the largest particles, where the deviation could reach as high as 0.21, signaling a significant alteration in the seal's performance. The simulations showed that the worst-case scenarios happened when larger particles happened to cluster near the most prominent peaks of the rough surface, creating a perfect storm of concentrated stress.

This work provides a clear, quantitative picture of why particle contamination is such a critical issue in deep-sea engineering. It moves beyond the simple idea that particles just wear down surfaces and shows how they fundamentally reshape the way forces are transferred at the microscopic level. By proving that particle size is the dominant factor over particle count, the study offers a new way for engineers to assess risk. They can now use these findings to predict how a seal will behave in a dirty environment and to design systems that are more robust against the specific sizes of debris likely to be encountered. The methods developed here, which combine realistic surface reconstruction with detailed contact analysis, provide a solid foundation for optimizing seals for the harsh, particle-filled conditions of the deep ocean, ensuring that the equipment used to explore our planet's resources remains secure.

Technical Summary: Sealing Performance of Particle-Adhered Rough Interfaces

Problem Statement
Solid-particle adhesion is a critical factor degrading sealing interfaces in particle-laden environments, such as subsea pressure-retaining coring, offshore oil and gas drilling, and pipeline transportation. In these applications, rock cuttings and suspended particles can become trapped within sealing interfaces (e.g., between a Y-ring seal and a core lifter case), damaging sealing surfaces and disrupting uniform pressure transmission. While existing literature has examined particle-induced wear and friction, many studies simplify metallic sealing surfaces as smooth or regular geometries. This simplification fails to capture the localized contact and non-uniform load transfer inherent to actual rough interfaces. Furthermore, a comprehensive approach to jointly evaluate the real contact area, normal contact force, and average contact pressure to quantify the overall deviation of the interfacial contact state under particle adhesion is currently lacking.

Methodology
To address these gaps, the study establishes an equivalent rough-surface reconstruction model incorporating particle adhesion and employs a three-dimensional finite-element method (FEM) contact model.

Equivalent Rough-Surface Reconstruction:
- A Gaussian rough morphology is numerically generated to represent the original metallic substrate.
- Particle adhesion is simulated by superimposing discrete particle geometries onto the original height field.
- A geometric correction term is introduced to account for local protrusions based on particle height, radius, and distribution density.
- A continuous smoothing operator ( $S_\sigma$ ) is applied to ensure spatial continuity and eliminate geometric discontinuities caused by direct superposition.
- A normalization step ensures the final equivalent surface retains the statistical roughness parameters (e.g., $R_a$ , $S_q$ ) of the original surface while reflecting local topographic changes.
- The model is validated against an explicit particle-adhered reference model using statistical metrics (height distribution, skewness, kurtosis), autocorrelation functions (ACF), and power spectral density (PSD).
Finite-Element Contact Analysis:
- A 3D FEM model simulates the contact between a polyurethane seal ring (modeled using a two-parameter Mooney–Rivlin hyperelastic model) and the reconstructed particle-adhered metallic surface (Q235 steel).
- The study investigates ten distinct models varying by particle coverage ( $C = 10\%, 30\%, 50\%$ ) and particle size ( $D = 1.25, 2.5, 5 \, \mu m$ ), with a particle-free condition serving as the baseline.
- Displacement-controlled loading is applied to simulate the sealing process, analyzing von Mises stress, contact pressure ( $P_{CPRESS}$ ), normal contact force ( $F_N$ ), real contact area ( $A_{real}$ ), and average contact pressure ( $P_{AVG}$ ).
Safety Margin Evaluation:
- A safety-margin deviation metric ( $SM_{dev}$ ) is proposed to quantify the overall deviation of the interfacial contact state relative to the particle-free baseline. This metric aggregates normalized variations in $A_{real}$ , $F_N$ , and $P_{AVG}$ .

Key Contributions

Reconstruction Model: Development of an equivalent rough-surface reconstruction method that preserves the statistical characteristics of the original rough surface while incorporating the local topographic modifications induced by particle adhesion.
3D FEM Contact Model: Establishment of a contact model between a seal ring and an equivalent rough metallic surface to characterize the evolution of contact states under varying particle sizes and coverages.
Safety-Margin Method: Proposal of a quantitative evaluation method based on the sealing contact state to assess the extent to which particle adhesion alters the interface, providing a basis for performance evaluation in particle-laden environments.

Results

Stress and Pressure Concentration: The dominant asperities of the original rough surface primarily determine the locations of contact-pressure and equivalent-stress concentrations. Particle adhesion intensifies these local concentrations and results in a more non-uniform load distribution.
Influence of Particle Size vs. Coverage: Particle size has a markedly greater influence on the interfacial contact state than particle coverage.
- At $D = 1.25 \, \mu m$ , variations in real contact area and normal contact force remain within 5%.
- At $D = 2.5 \, \mu m$ , the real contact area increases by approximately 9%, and the normal contact force increases by 8–14%.
- At $D = 5 \, \mu m$ , both the normal contact force and average contact pressure increase by 15–25%.
Safety Margin Deviation ( $SM_{dev}$ ):
- For $D = 1.25 \, \mu m$ , $SM_{dev}$ generally remains below 0.03, indicating minimal impact on the overall contact state.
- For $D = 2.5 \, \mu m$ , $SM_{dev}$ increases to approximately 0.09 with increasing coverage.
- For $D = 5 \, \mu m$ , deviations are significantly larger overall. The maximum deviation ( $SM_{dev} = 0.21$ ) occurs at 30% coverage, suggesting that the spatial distribution of particles relative to dominant asperities plays a critical role, and that increasing coverage does not always linearly increase deviation.

Significance
The study provides a methodological basis for the performance evaluation and structural optimization of sealing interfaces operating in particle-laden environments. By preserving the characteristics of the original rough surface while quantitatively evaluating the effects of particle size and coverage, the proposed framework offers a theoretical foundation for designing sealing systems for marine exploration, oil and gas pipeline transportation, and related engineering applications where solid-particle contamination is inevitable. The authors note that further work involving controlled experiments and additional stochastic surface realizations is required to refine safety-margin thresholds and establish the full applicability range of the model.

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