Finite Element-Based Optimisation of Two-Stroke Marine Diesel Piston: A structural reliability and weight reduction study

 Corresponding author: Koko Edwin Preye Copyright © 2025 Author(s) retain the copyright of this article. This article is published under the terms of the Creative Commons Attribution License 4.0. Finite Element-Based Optimisation of Two-Stroke Marine Diesel Piston: A structural reliability and weight reduction study Koko Edwin Preye * and Ajoko Tolumoye John Department of Mechanical Engineering, Niger Delta University, PMB 71, Bayelsa State, Nigeria. Global Journal of Engineering and Technology Advances, 2025, 23(02), 239–254 Publication history: Received on 08 April 2025; revised on 27 May 2025; accepted on 30 May 2025 Article DOI: https://doi.org/10.30574/gjeta.2025.23.2.0165 Abstract Two-stroke marine diesel engines are pivotal in propelling ocean-going vessels, owing to their remarkable efficiency and durability. Within these engines, the piston is subjected to extreme mechanical and thermal loads, positioning it as a critical component for structural optimisation. This study presents a simulation-driven design optimisation of a marine two-stroke piston to enhance mechanical performance while reducing component weight. A parametric model was developed using SolidWorks, and the Taguchi method was applied to investigate the effects of piston height, crown thickness, and pin diameter on displacement, von Mises stress, factor of safety (FOS), and overall mass. Finite element analysis (FEA) was conducted under a peak combustion pressure of 15.3 MPa, with model validation achieved through a Grid Convergence Index (GCI)-based mesh independence study. The analysis indicated crown thickness was the most influential factor affecting piston stiffness and stress behaviour. The optimised design, featuring a height of 1000 mm, crown thickness of 120 mm, and pin diameter of 300 mm in alloy steel, achieved a 25.7% reduction in weight while maintaining a maximum von Mises stress of 2.94 × 10⁸ N/m² and an FOS of 6.05. These results illustrate the effectiveness of combining parametric modelling with statistical optimisation to achieve lightweight and structurally resilient piston designs suitable for high-load marine diesel applications. Keywords: Piston design optimisation; Finite element analysis (FEA); Taguchi method; Von Mises stress; Factor of safety (FOS); Weight reduction 1. Introduction Twostroke marine diesel engines remain the backbone of longhaul maritime propulsion systems due to their high thermal efficiency, powertoweight ratio, and operational reliability for large cargo vessels and tankers (Zhang et al., 2025; ElSayed & Wang, 2023). The piston is subjected to the most severe combination of thermal and mechanical loads among all internal components due to direct exposure to combustion gases, rapid pressure cycles, and substantial inertial forces during reciprocating motion (Chen et al., 2024; Lin et al., 2022). Failures in piston crowns, pin bosses, and skirts are often linked to inadequate stress distribution, excessive deformation, or suboptimal material selection. Consequently, ensuring structural integrity through robust design and accurate stress analysis is critical for minimising the risks of fatigue, thermal cracking, and wear (Yang et al., 2023; Wang et al., 2022). Recent advancements in finite element analysis (FEA) tools have enabled engineers to simulate such stress responses under realistic loading conditions, allowing for more reliable performance predictions and component optimization (Kim & Cho, 2024; Park et al., 2023). While several studies have focused on componentlevel modelling of diesel engine parts, there remains a gap in design optimisation that simultaneously targets weight reduction, improved stiffness, and safety margin enhancement under Global Journal of Engineering and Technology Advances, 2025, 23(02), 239–254 240 static loads (Zhang et al., 2025; Uchenna & Godwin, 2025). Furthermore, most research efforts concentrate on generalpurpose automotive pistons, leaving a gap in detailed structural analysis specific to largescale marine twostroke pistons operating under more demanding mechanical conditions. This study aims to bridge this gap by developing and evaluating an optimised piston design for a twostroke marine diesel engine. The methodology integrates parametric modelling, FEAbased stress analysis, comparative displacement, weight, and safety factor evaluation. The proposed optimisation reduces weight while maintaining acceptable stress levels and structural reliability. 2. Methodology This study adopted a systematic design and simulation approach to optimise a two-stroke marine diesel engine piston for improved structural reliability and reduced weight under static mechanical loading. The methodology comprises three phases: parametric design formulation, 3D CAD modelling, and finite element-based stress analysis. 2.1. CAD Modelling Using SolidWorks and Material Selection All piston variants were designed using SolidWorks 2018, leveraging parametric design capabilities to enable automated dimension adjustments. Each model incorporated crucial geometric details, including the piston crown, skirt pin boss, and cooling gallery (excluded from the stress zone). Dimensional inputs from the Taguchi design table were seamlessly integrated into SolidWorks via linked design tables, allowing for rapid CAD generation of all configurations. 2.2. Finite Element Analysis (FEA) in SolidWorks Simulation SolidWorks Simulation Professional was used for static FEA of each piston model under maximum combustion pressure loading. This choice allowed seamless transition from CAD to analysis while preserving geometric fidelity. Table 1 Boundary Conditions for FEA of Piston Design Condition Type Description Value / Setting Applied To Load Static pressure simulating peak combustion load 15.3 MPa (uniform) Piston crown (top surface) Support Constraint simulating connection with the connecting rod Fixed geometry Inner surfaces of the pin boss Material Assignment Defined based on the selected design material Alloyed steel / Carbon steel / Stainless steel Entire piston body Contact Condition Bonded contact (no relative motion between parts) Fine mesh Entire body Mesh Type Tetrahedral mesh with adaptive refinement Curvature-based, fine around stress zones Full piston geometry Element Size Target size based on the convergence study 3–5 mm (local refinement at pin boss) Crown edges, pin boss Solver Type Static linear solver Direct sparse solver Entire simulation domain Gravity (optional) Self-weight is included in specific weight estimation runs 9.81 m/s² Global 2.3. Governing Equations and Design Optimisation Using the Taguchi Method The governing equations for thermo-mechanical behaviour were based on the Navier-Cauchy equilibrium equation and linear elasticity. Postprocessing focused on extracting the maximum von Mises stress and displacement. Global Journal of Engineering and Technology Advances, 2025, 23(02), 239–254 241 2.4. Structural and Thermo-Mechanical Governing Equations The laws of linear elasticity govern the stress and deformation behaviors of the piston under thermo-mechanical loading. The equilibrium equation for a 3D solid is expressed as: ∇ × 𝜎+ 𝐹 = 0 ……………..(1) Assuming quasi-static conditions and negligible body forces: ∇ × 𝜎 = 0 …………… (2) The stress–strain relationship (Hooke’s Law) for isotropic, linear elastic materials is: Total strain is: 𝛆 = 1 2(∇ × 𝐮 + (𝛁𝐮)𝑻) ……………. (3) Thermal and combustion loads are applied on the piston crown as pressure and temperature boundary conditions. The system is solved using finite element methods (FEM) in SolidWorks software. 𝜎 = 𝐶 × (𝜀 −𝜀𝑡ℎ𝑒𝑟𝑚𝑎𝑙) …………. (4) Where, σ =Stress tensor, ε= total strain tensor, 𝜀𝑡ℎ𝑒𝑟𝑚𝑎𝑙 = 𝛼(𝑇 −𝑇0)I thermal strain, C elasticity tensor, α= thermal expansion coefficient 2.5. Design Optimisation via Taguchi Method To optimise the piston’s geometry for weight reduction and stress minimisation, the Taguchi design of experiments (DOE) method was employed. The Taguchi method uses orthogonal arrays (OAS) to study the influence of multiple design parameters with fewer simulations. It evaluates the sensitivity of responses to input factors and identifies optimal parameter settings. The quality characteristic selected in this study is “Smaller is Better” for both stress and displacement: 2.6. Grid Independence and GCI Analysis A grid sensitivity analysis used coarse, medium, and fine meshes (2,258, 8,576, and 56,927 elements). Displacement and stress were selected as monitoring parameters. The Grid Convergence Index (GCI) was calculated using Richardson extrapolation, revealing less than 1% error between the fine and medium meshes. Thus, the medium mesh was adopted for all DOE runs to balance computational cost and accuracy. The GCI values for the Fine-Medium and Medium-Coarse grids were calculated using Eqn. 5: 𝐺𝐶𝐼 = 1.25×|𝑓2−𝑓1| 𝑟𝑝−1 ×100 ………….(5) Where, 𝑓2 and 𝑓1 The simulation outcomes for two adjacent meshes are represented by the symbols r and p. The symbol r denotes the refinement ratio, and p signifies the assessed order of accuracy. 2.7. Grid Independence and Discretisation Error Estimation A grid independence study was conducted to ensure the finite element results were not sensitive to mesh resolution. Three structured meshes were used: coarse (2,258 elements), medium (8,576 elements), and fine (56,927 elements). The study focused on the von Mises stress and maximum displacement as primary output variables. The Grid Convergence Index (GCI) method recommended by ASME was employed to quantify the numerical uncertainty due to discretisation. This method uses Richardson extrapolation and estimates the apparent order of convergence p and the relative error between meshes levels. 2.8. Design of Experiments Using the Taguchi Method A systematic Taguchi Design of Experiments (DOE) approach was implemented using Design Expert 13 software to reduce the number of simulations runs while capturing the effect of key piston design variables. Three input parameters, Global Journal of Engineering and Technology Advances, 2025, 23(02), 239–254 242 piston height (A), crown thickness (B), and pin diameter (C), were selected at three levels each. The selected factors and their levels are shown in Table 2. Table 2 Experimental Design Factors and Levels Factor Level 1 Level 2 Level 3 A: Height (mm) 1000 1200 1400 B: Thickness (mm) 80 100 120 C: Pin Diameter (mm) 300 350 400 Material Alloy steel Stainless Steel Carbon steel An L9 orthogonal array was generated, resulting in nine design combinations for simulation. This experimental design allowed for the investigation of the main and interaction effects on structural displacement, factor of safety (FOS), von Mises stress, and mass. 2.9. Optimisation and Validation The S/N ratio results were analysed to identify the most influential factors of stress and displacement. An analysis of Variance (ANOVA) was performed to determine statistical significance. Based on the maximum S/N ratios, the optimal design combination was selected, and a confirmation run was conducted using this design. The final optimised piston design showed significant improvements in structural reliability and performance. 𝑆𝑁 ⁄ = −10𝑙𝑜𝑔1 𝑛(∑1 𝑦2) ……………….. (6) The response table for each quality characteristic has been prepared to determine the best combination of parameters, based on the S/N ratio and contribution of each quality characteristic. Figure 1 Tetrahedral mesh with adaptive refinement around the crown and pin boss. Element quality verified using mesh convergence checks 3. Results and Discussion 3.1. Grid Independence Study Result A systematic grid independence analysis was conducted on three progressively refined meshes: coarse (2,258 elements), medium (8,576 elements), and fine (56,927 elements), to quantify discretisation uncertainty using the ASMErecommended Grid Convergence Index (GCI) method. Table 1 summarises the observed orders of convergence and GCI values between the fine and medium meshes for both von Mises stress and maximum displacement. Global Journal of Engineering and Technology Advances, 2025, 23(02), 239–254 243 Table 3 Grid Independence Study Parameter Order of Convergence, p GCI₍₂₁₎ (%) von Mises Stress 6.15 0.044 Displacement 2.43 0.592 Table 4. Observed convergence orders and GCI values between fine and medium meshes. The stress field shows a high convergence rate (p = 6.15) and an extremely low GCI (0.044 %), indicating that mesh refinement beyond medium density results in negligible changes in peak stress predictions. Displacement converges gradually (p = 2.43) but still achieves GCI < 1 %, confirming that the medium mesh accurately captures global deformations within acceptable numerical uncertainty. Based on these results, the medium mesh (8,576 elements) was adopted for all subsequent simulations, providing a robust compromise between computational efficiency and solution fidelity. Table 4 Taguchi Analysis: Displacement (mm), FOS, Weight (Kg) versus Height (mm), Thickness (mm), Pin dia. (mm), Material Run Height (mm) Thickness (mm) Pin dia. (mm) Material Displacement (mm) FOS Von Mises Stresses (N/m2) Weight (Kg) 1 1400 120 350 Alloy steel 0.5238 6.133 2.738×108 3594 5 1400 100 300 Stainless steel 0.9178 5.232 3.711×108 3178 2 1400 80 400 Carbon steel 1.6230 5.261 5.425×108 2573 9 1200 120 300 Carbon steel 0.5498 5.303 2.840×108 3197 4 1200 100 400 Alloy steel 0.8291 5.791 3.922×108 2667 8 1200 80 350 Stainless steel 1.6700 5.155 5.551×108 2219 6 1000 120 400 Stainless steel 0.5060 5.286 3.015×108 2595 7 1000 100 350 Carbon steel 0.8275 5.274 4.026×108 2595 9 1000 80 300 Alloy steel 1.5960 5.524 5.916×108 1911 Table 5 presents the S/N ratio analysis based on the "larger is better" criterion, which reveals that crown thickness strongly influences the performance response, as indicated by the highest Delta value (9.4640) and Rank 1 position. Pin diameter ranks second, followed by piston height, while material type shows the least impact on the output response. This implies that optimising the thickness parameter is most crucial for improving structural reliability, stiffness, and safety margins. The data support prioritising geometric tuning (particularly thickness and pin size) over material changes in the early-stage optimisation of the piston design. Table 5 Response for Signal-to-Noise Ratios Level Height (mm) Thickness (mm) Pin dia. (mm) Material 1 3.4397 8.6195 3.9690 3.5540 2 3.7921 3.3236 3.6453 3.7109 3 3.8668 -0.8445 3.4842 3.8338 Delta 0.4270 9.4640 0.4848 0.2798 Rank 3 1 2 4 Figure 2 displays the main effects plot, demonstrating that both piston height and crown thickness have a significant influence on the system's response, as evidenced by their steep slopes. Specifically, raising the piston height from 1000 mm to 1400 mm consistently increases the mean response, likely due to the added mass and deformation linked with taller pistons. Likewise, enhancing thickness from 80 mm to 120 mm boosts performance by reducing displacement and Global Journal of Engineering and Technology Advances, 2025, 23(02), 239–254 244 increasing stiffness. In contrast, the pin diameter and material type exhibit relatively flatter trends, indicating a lesser impact within the tested range. Among the materials, carbon steel shows a slight advantage over alloyed and stainless steels under the specified loading conditions. This analysis emphasises the importance of geometric parameters, particularly height and thickness, for future optimisation. Figure 2 Main effects plot for the mean performance displacement, FOS, and stress. Across different levels of design factors. The plot shows the influence of Height, Thickness, Pin diameter, and Material on the output response 3.2. Analysis of Variance Table 6 ANOVA for the Deformation Source Sum of Squares df Mean Square F-value p-value Model 1.91 6 0.3178 26.18 0.0372 significant A-Piston Height 0.0500 2 0.0250 2.06 0.3269 B-Piston Thickness 1.90 2 0.9507 78.31 0.0126 C-Piston pin 0.0425 2 0.0212 1.75 0.3636 Residual 0.0243 2 0.0121 Cor Total 1.93 8 The Model F-value of 26.18 implies that the model is significant. There is only a 3.72% chance that an F-value this large could occur due to noise. P-values less than 0.0500 indicate that model terms are significant. In this case, B is a significant model term. Values greater than 0.1000 indicate that model terms are not significant. If there are many insignificant model terms (excluding those required to support hierarchy), model reduction may improve your model, as shown in Table 7. Table 7 ANOVA for the Von Mises Stress Source Sum of Squares df Mean Square F-value p-value Model 6.635E+07 2 3.318E+07 39.15 0.0004 significant B-Piston Thickness 6.635E+07 2 3.318E+07 39.15 0.0004 Residual 5.085E+06 6 8.474E+05 Cor Total 7.144E+07 8 Global Journal of Engineering and Technology Advances, 2025, 23(02), 239–254 245 The Model F-value of 39.15 indicates that the model is significant. There is only a 0.04% chance that an F-value this large could occur due to random noise. P-values less than 0.0500 suggest that the model terms are essential. In this case, B is a significant model term. Values greater than 0.1000 imply that the model terms are not significant. If there are many insignificant model terms (excluding those required to maintain hierarchy), model reduction may enhance your model. Table 8 ANOVA for the weight of the piston Source Sum of Squares df Mean Square F-value p-value Model 2.146E+06 4 5.364E+05 130.00 0.0002 significant A-Piston Height 5.196E+05 2 2.598E+05 62.96 0.0009 B-Piston Thickness 1.302E+06 2 6.510E+05 157.76 0.0002 Residual 16504.83 4 4126.21 Cor Total 2.162E+06 8 The Model F-value of 130.00 indicates that the model is significant. There is only a 0.02% chance that an F-value this large could occur due to random noise. P-values less than 0.0500 suggest that the model terms are essential. In this case, A and B are significant model terms. Values greater than 0.1000 indicate that the model terms are not significant. If there are many insignificant model terms (excluding those required to support hierarchy), model reduction may enhance your model. The predicted mean and median may differ from the original scale for transformed responses. Standard error (SE) is not calculated on the original scale, as illustrated in Table 8. Table 9 Confirmation Two-sided Confidence = 95% Solution 1 of 20 Response Predicted Mean Predicted Median* Std Dev n SE Pred 95% PI low 95% PI high Deformation 0.36715 0.36715 0.110181 1 0.166794 -0.350507 1.08481 Factor of Safety 5.43989 5.43989 0.323473 1 0.34097 4.65361 6.22617 Von Mises Stress 2.79724E+08 2.78877E+08 3.07696E+07 1 N/A 1.94346E+08 3.78629E+08 weight of the piston 3005 3005 64.2356 1 93.0862 2746.55 3263.45 The predicted mean and median for transformed responses may differ from those on the original scale. The data mean is calculated on the transformed scale, while the standard error (SE) is not determined on the original scale. As shown in Table 9. Table 10 Comparison of Baseline and Optimal Design Design Height (mm) Thickness (mm) Pin dia. (mm) Material Displacement (mm) FOS Stresses (N/m2) Weight (Kg) Baseline Design 1400 120 350 Alloyed steel 0.5238 6.133 2.738×108 3594 Optimal Design 1000 120 300 Alloyed steel 0.367 5.440 279724128.129 3005.000 Figure 3 illustrates the primary effects of piston height (A) on various performance metrics while keeping other variables constant (B = 120, C = 300, D = Alloy steel). As piston height increases from 120 mm to 140 mm, Desirability displays a sharp decline from 0.84 to 0, indicating that a height of 140 mm corresponds to a significantly less favourable design. Distortion slightly increases, predicting 0.36715 mm at 120 mm, which suggests improved dimensional stability at lower heights. The factor of Safety remains constant at 5.43989, indicating no sensitivity to variations in piston height within this range. Stress remains unchanged at 2.79724e+08 N/m², with height exerting no influence. Additionally, Piston Weight rises from approximately 3005 g as height increases, which is expected due to the additional material used. Global Journal of Engineering and Technology Advances, 2025, 23(02), 239–254 246 Figure 3 One-factor analysis of piston height (Factor A) on performance responses, including desirability, distortion, factor of safety, stress, and weight, under fixed conditions (B = 120, C = 300, D = Alloy steel) Figure 4 illustrates that the interaction between piston height and thickness significantly impacts the piston's overall performance. The most desirable configuration occurs at the highest tested levels—120 mm for both height and thickness where desirability reaches 0.84 and distortion minimises to 0.36715 mm. This indicates a strong positive interaction, where both factors work synergistically to enhance performance. While the factor of safety (5.43989) and stress (2.79724e+08 N/m²) remain largely unaffected by these changes, the piston weight increases noticeably with both dimensions, reaching a maximum of 3005 g at the optimal configuration. Increasing piston height and thickness improves performance and dimensional stability; however, designers must balance this with the resulting weight increase. Global Journal of Engineering and Technology Advances, 2025, 23(02), 239–254 247 Figure 4 Interaction effects of piston height (Factor A) and piston thickness (Factor B) on performance metrics including desirability, distortion, safety factor, stress, and piston weight. Figure 5 presents 3D response surface matrix plots that illustrate the combined influence of piston height (A) and piston thickness (B) on five performance metrics: Desirability, Deformation, Factor of Safety, Stress, and Weight under fixed conditions (C = 300, D = Alloy steel). Each subplot shows how various combinations of A and B affect the outcomes. Desirability is maximised (0.84) at A = 120 mm and B = 120 mm, decreasing sharply as both variables decrease, particularly when both are at their lowest (A = 140 mm, B = 80 mm). Deformation is minimised (0.36715 m) at the same optimal condition (A = 120 mm, B = 120 mm) and increases slightly with lower B values. Factor of Safety remains constant at 5.43989 across all combinations, indicating robustness to changes in A and B. Stress also shows minimal variation (2.79724e+08 N/m²), further confirming structural stability. Weight increases steadily from 2950.47 g at (A = 120 mm, B = 80 mm) to 3005.48 g at (A = 140 mm, B = 120 mm), consistent with the added material volume. Global Journal of Engineering and Technology Advances, 2025, 23(02), 239–254 254 [6] Uchenna, B. A., & Godwin, O. (2025). 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