The research, conducted by H. R. Alimohammadi and H. Naseh of the Aerospace Research Institute in Tehran and F. Ommi of Tarbiat Modares University, focuses on the design optimization of a thrust chamber for the RD-161 propulsion system. The team set out with two objective functions at the center of the work: specific impulse, which measures how efficiently propellant is converted into thrust, and thrust-to-weight ratio, which captures how much acceleration an engine can deliver for the mass it adds to the vehicle. These two quantities are widely regarded as the defining figures of merit for liquid-propellant engines, and they frequently pull the design in opposite directions. A chamber shaped for maximum exhaust velocity may end up heavy; a lightweight design may sacrifice combustion efficiency.

To formalize the problem, the researchers identified seven input variables that govern the geometry and operating conditions of the chamber: the propellant consumption ratio, the combustion chamber pressure, the contraction area ratio between the chamber cross-section and the throat, the expansion pressure ratio across the nozzle, two geometric ratios describing the convergence of the chamber walls, and the contraction angle itself. Together, these parameters define a vast multidimensional design space in which even a modest number of candidate configurations quickly becomes computationally overwhelming. Evaluating every possible combination with high-fidelity physics simulations would require an impractical amount of time and computing resources, which is precisely the bottleneck the surrogate approach is designed to remove.

A surrogate model, sometimes called a metamodel, is essentially a fast mathematical approximation of a slower, more expensive simulation. Instead of running a full physics-based analysis for every candidate design, engineers run a strategically chosen subset of simulations and then fit a statistical model that interpolates the results across the entire design space. The quality of the surrogate depends critically on how those sample points are selected, which is where the Design of Experiments methodology comes in. In this study, the team carried out 46 different numerical experiments on the RD-161 propulsion system, varying the seven input parameters according to a structured experimental plan. Of those 46 runs, 39 produced results that were approved and found compatible with the problem constraints, forming the data foundation on which the response surfaces were built.

From that approved dataset, the researchers drew response surface curves and derived the corresponding objective function equations that link the seven input variables to the two performance outputs. Response surfaces are a powerful visualization and analysis tool because they reveal not just the optimum point but the entire topology of the design landscape: where performance rises steeply, where it plateaus, and where design variables interact in ways that a one-at-a-time sensitivity study would miss. The team then applied the Analysis of Variance, or ANOVA, to quantify how much of the variation in specific impulse and thrust-to-weight ratio could be attributed to each input factor and their combinations. According to the published results, the ANOVA demonstrated that the model is capable of predicting the responses adequately within the limits of the input parameters, a crucial validation step before any optimization can be trusted.

The precision of the fitted model was assessed against independent checks, and the authors report that the outputs showed high accuracy when interpreted and analyzed. With a validated surrogate in hand, the optimization itself could proceed far more efficiently than a brute-force sweep of the design space. The study notes that classical optimization techniques such as Genetic Algorithms and Sequential Quadratic Programming are commonly paired with surrogate models in this domain, allowing search algorithms to evaluate thousands of candidate configurations on the cheap statistical approximation while reserving full simulations for the most promising regions. This combination is what makes multidisciplinary design optimization of rocket engines practical on realistic engineering timescales.

The headline results are striking for a field where gains are often measured in fractions of a percent. Applying the methodology to optimize the thrust chamber, the researchers achieved a 2.8-second increase in specific impulse and an 8.5 percent increase in thrust-to-weight ratio for the chamber itself. When the objective functions were evaluated at the level of the complete engine, the improvements grew even larger: specific impulse rose by 3 seconds and the thrust-to-weight ratio climbed by 12 percent. In the conservative world of liquid-propellant engine design, where flight-proven hardware changes slowly and every design revision must survive rigorous qualification, improvements of this magnitude are considered considerably large, and they illustrate how much performance may be left on the table when chambers are designed by iteration and experience alone rather than systematic global optimization.

The work also sits within a broader movement in propulsion engineering toward simulation-driven, data-rich design. Earlier studies have applied genetic algorithms, particle swarm methods, and mass-based models to liquid rocket engine design problems, and the same research group has previously developed surrogate-based frameworks for optimizing the cooling systems and multidisciplinary robust design of liquid-propellant engines. Regenerative cooling channels, turbine design, and combustion modeling have all been drawn into multidisciplinary optimization frameworks in recent years, reflecting a recognition that the classical separation of engine components into isolated design silos leaves coupled performance gains undiscovered. The surrogate approach presented here extends that trajectory to one of the most consequential components in the entire engine.

What makes the surrogate methodology especially attractive for engineering practice is that it produces not just a single optimized point but an interpretable map of the design space, complete with objective function equations that other teams can reuse and adapt. The response surfaces can expose trade-off frontiers between specific impulse and mass, guiding engineers toward designs that best serve a particular mission profile rather than a generic ideal. The study also underscores the importance of constraint filtering: of the 46 experiments conducted, 7 fell outside the problem constraints and were excluded, a reminder that raw computational sweeps are only as useful as the feasibility boundaries that frame them. Careful constraint definition, the authors’ results suggest, is as essential to credible optimization as the statistical model itself.

For the wider aerospace community, the implications extend beyond the RD-161. As launch providers pursue reusable boosters and satellite operators demand ever more capable propulsion for orbit-raising and station-keeping, the pressure to extract maximum performance from minimum mass will only intensify. Surrogate-based design optimization offers a path to that performance without the prohibitive cost of exhaustive high-fidelity simulation, and the substantial gains reported in this study provide concrete evidence that the approach is ready to move from academic methodology into the engine design offices where the next generation of liquid-propellant engines will take shape. The datasets generated and analyzed in the study are available from the corresponding author on reasonable request, opening the door for other groups to build on the framework.

Subject of Research: Surrogate model development for the design optimization of a liquid-propellant rocket engine thrust chamber

Article Title: A surrogate model development for design optimization of thrust chamber

Article References: Alimohammadi, H. R., Naseh, H., & Ommi, F. (2026). A surrogate model development for design optimization of thrust chamber. Aerospace Systems. https://doi.org/10.1007/s42401-026-00548-0

Image Credits: AI Generated

DOI: 10.1007/s42401-026-00548-0

Keywords: surrogate model, thrust chamber, liquid-propellant engine, design optimization, specific impulse, thrust-to-weight ratio, response surface methodology, ANOVA, Design of Experiments, rocket propulsion, Aerospace Systems, RD-161

Investment casting is one of metallurgy’s oldest processes, with roots stretching back to early weapons, jewelry, and religious art. It remains prized today for aerospace turbine blades and biomedical components because it delivers exceptional surface finish, dimensional accuracy, and the ability to reproduce complex shapes. In Nepal, the technique has been used since at least the sixth century A.D. to produce the bronze and gilded deities that fill temples and monasteries across the Himalayas. The process is intensely manual: a sculptor first carves a detailed wax master pattern, which is encased in a rubber mold from which multiple wax replicas can be made. These replicas are assembled with gating systems, dipped in a traditional slurry of cow dung and clay, reinforced with metal wires, dewaxed, preheated, and finally filled with molten metal. After cooling, each piece demands hours of filing, chiseling, and hand-applied gold plating.

That artisanal character comes at a cost. Defect rates in Nepali sculpture casting hover around thirty percent, and sculptures can take anywhere from one month to two years to complete depending on size. Because global economic shifts and advancing technology are squeezing demand for Nepali cast sculptures, improving casting design, modeling, and production efficiency has become essential for the industry’s survival. The research team, led by Zenisha Shrestha with Abhishek Pandey and Bijendra Prajapati, set out to determine whether systematic parameter optimization, never before applied to this traditional setting, could meaningfully improve dimensional accuracy in gilding metal, an alloy of ninety percent copper and ten percent zinc that is the most widely used sculpture material in Nepal.

The researchers chose a sword as their test specimen, selected for its cultural relevance in Nepali society and its relatively simple geometry, which makes dimensional analysis tractable. The design was modeled in SOLIDWORKS, with the gating system developed through the modulus method to reflect designs typical of sculpture manufacturing. From an Ishikawa cause-and-effect analysis of casting stability, the team identified three controllable parameters: the number of slurry coating layers, the mold preheat temperature, and the metal pouring temperature. Factors such as wax composition, alloy composition, slurry composition, cooling methods, and environmental conditions were treated as noise parameters that could not be easily controlled in the workshop.

The experimental design followed a Taguchi L9 orthogonal array, allowing nine carefully chosen experiments to explore the parameter space efficiently. Slurry coatings ranged from two to four layers, preheat temperatures spanned 500 to 600 degrees Celsius, and pouring temperatures covered the 1150 to 1200 degree Celsius range typical of Nepali sculpture foundries. Each coating choice involves a trade-off: thin shells save material and time but risk bulging and leaking under the metallostatic pressure of pouring, while thicker coatings prevent defects and improve heat retention at the cost of longer processing. Preheating the mold reduces thermal shock and premature freezing of the melt, improving fill of thin sections, though excessive preheat can accelerate mold-metal reactions and increase surface-connected porosity. Higher pouring temperatures superheat the metal above its melting point, preventing unfilled sections in intricate features.

Four response variables were measured for each casting: weight, length, breadth, and thickness. Before optimization, the team verified data quality through normality testing with probability plots and the Anderson-Darling test, confirming that all responses followed normal distributions. Pareto tests and analysis of variance at a 95 percent confidence level then established that all three process parameters significantly influenced every response variable. The number of coatings emerged as the dominant factor, contributing 44.42 percent of the variance in weight, 48.01 percent in length, 58.81 percent in breadth, and 41.82 percent in thickness. Pouring temperature exerted its greatest influence on weight at 39.31 percent and length at 31.38 percent, while preheat temperature most strongly affected breadth and thickness. Residual plots showed randomly distributed errors, confirming the reliability of the statistical model.

Because dimensional accuracy depends on optimizing all four responses simultaneously, the researchers turned to multi-response optimization. Grey relational analysis, a technique designed for systems with limited information, converts multiple responses into a single grey relational grade by normalizing the data and calculating correlation coefficients, using an identification coefficient of 0.5 consistent with prior studies. The innovation here was the coupling of grey relational analysis with principal component analysis, which uses eigenvectors to derive objective weights for each response rather than assuming they matter equally. The first principal component captured 81.9 percent of the data’s variance and identified length as the most significant response. Experiment 3, combining a 500 degree Celsius preheat, a 1200 degree Celsius pour, and four coating layers, ranked highest under both the standard and PCA-weighted grades, and both methods converged on the same optimal setting, strengthening confidence in the result.

The confirmatory experiment delivered striking improvements. The weighted grey relational grade rose from 0.357 under initial conditions to 0.966 under optimal conditions, closely matching the predicted value of 0.9677. Weight deficit fell from 3.160 percent to 0.682 percent, length shrinkage dropped from 4.860 percent to 0.545 percent, breadth shrinkage plummeted from 6.156 percent to 1.067 percent, and thickness shrinkage declined from 4.200 percent to 1.800 percent. In practical terms, a cast sword produced under the optimized parameters now deviates from its wax pattern by barely one percent in its principal dimensions, meaning far less manual filing and correction before gold plating. Given that finishing work is among the most labor-intensive stages of sculpture production, even modest dimensional improvements translate into significant reductions in lead time and cost.

The implications extend well beyond Nepal’s foundries. The authors note that the GRA-PCA methodology can be adapted to any complex manufacturing process where multiple conflicting objectives must be balanced, including precision casting of aerospace turbine blades, biomedical device manufacturing where dimensional control is critical, and automotive component casting where strength, weight, and tolerances compete. For Nepal, the study represents the first application of advanced multi-response optimization to traditional sculpture casting, and it arrives at a pivotal moment for an industry whose economic viability depends on competing with industrialized producers. Future work, the researchers suggest, could examine surface roughness, mechanical properties, and additional process parameters. But the central message is already clear: fourteen centuries of artisanal wisdom and twenty-first-century statistical rigor are not adversaries. When the number of coatings, the preheat temperature, and the pouring temperature are tuned together, the ancient art of Himalayan metal sculpture can achieve a precision its original masters could scarcely have imagined, preserving both a cultural heritage and the livelihoods of the craftsmen who sustain it.

Subject of Research: Multi-response optimization of investment casting parameters to improve the dimensional accuracy of gilding metal sculptures in traditional Nepali manufacturing.

Article Title: Improvement of dimensional accuracy in gilding metal sculpture manufacturing using grey relational analysis coupled with principal component analysis

Article References: Shrestha, Z., Pandey, A., & Prajapati, B. (2026). Improvement of dimensional accuracy in gilding metal sculpture manufacturing using grey relational analysis coupled with principal component analysis. Heliyon, 12(14), Article e45412. https://doi.org/10.1016/j.heliyon.2026.e45412

Image Credits: AI Generated

DOI: Not provided

Keywords: investment casting, grey relational analysis, principal component analysis, Taguchi method, dimensional accuracy, gilding metal, Nepal sculpture manufacturing, shrinkage reduction, ANOVA, multi-response optimization, Kathmandu Valley, metal casting

The choice of matrix alloy was deliberate. AA6061 is a wrought aluminium alloy prized for its excellent thermal and physical properties, its corrosion resistance, and the ease with which it can be fabricated into machine parts, structural elements and aerospace components. Yet like most commercial alloys, it has limits in strength and wear performance that can restrict its use in demanding tribological applications such as brakes, bearings and gears. Materials scientists have long explored ways to tailor aluminium by adding hard ceramic or mineral particles, including silicon carbide, alumina, fly ash, red mud and zircon silicate, and previous studies have generally found that such reinforcements boost hardness and strength while often reducing density. What makes the new work distinctive is the use of marble dust, an abundant industrial waste stream from Rajasthan’s stone industry, which turns a disposal problem into a feedstock for advanced materials.

To create the composites, the team used a semi-automatic stir-casting process, one of the most economical and widely adopted liquid-state fabrication routes for metal matrix composites. Cleaned and cut AA6061 alloy rods were melted in a graphite crucible at 720 degrees Celsius, and the molten metal was fluxed to remove impurities. Around 2 weight percent of magnesium, added in the form of MgO, was stirred into the melt to improve wettability, a critical step because poorly wetted particles tend to cluster rather than disperse. Meanwhile, the marble dust was preheated to about 400 degrees Celsius for half an hour to drive off moisture and lower the surface energy of the particles, which further promotes uniform mixing. The heated reinforcement was then added incrementally while a graphite stirrer agitated the melt at 250 revolutions per minute for five minutes. The melt was superheated slightly to maintain fluidity and poured into a permanent mould, producing cast plates from which standard test specimens were machined.

Five compositions were prepared, spanning 0 to 6 weight percent marble dust in 1.5 percent increments, labelled M0 through M6. The researchers evaluated density, void content, tensile strength, flexural strength, hardness and impact strength for each formulation. A clear trend emerged: as the marble dust content increased, the void fraction dropped from roughly 12.5 percent to 6.66 percent, while every measured mechanical property improved. Tensile strength rose from about 238 megapascals in the unreinforced alloy to roughly 277 megapascals at 6 percent reinforcement. Hardness climbed from 75 to 90 on the Rockwell B scale, flexural strength increased from 180 to about 205 megapascals, and impact strength grew from 16.5 to 21 kilojoules per square metre. The team attributes these gains to two mechanisms: the rising dislocation density and the build-up of a stronger matrix-particle interface, which reduces voids and improves load transfer, and the ability of hard particles to act as barriers to dislocation motion, producing classic dispersion strengthening.

The tribological behaviour of the composites was assessed under dry sliding conditions, with the specific wear rate ranging from about 2.006 to 2.528 times ten to the minus six cubic millimetres per newton-metre. Three operating variables were systematically varied: normal load from 10 to 50 newtons, sliding distance from 800 to 4000 metres, and sliding velocity from 1 to 2 metres per second. Across the composition range, wear rate and friction coefficient increased with each of these parameters but fell as marble content rose. The M6 composite, containing the maximum 6 weight percent reinforcement, consistently delivered the lowest wear and friction. The researchers explain this through the same microstructural logic that governs the mechanical results: fewer voids mean a more continuous, better-bonded material that transfers load efficiently between matrix and particles, so the surface resists softening, ploughing and debris generation during sliding.

Scanning electron microscopy of the worn surfaces revealed the underlying wear mechanisms in vivid detail. At the lowest load of 10 newtons, the M6 composite displayed clean primary surfaces with minimal debris, evidence of its intactness and strength. At 20 newtons, mild ploughing and pitting appeared, and by 30 newtons deep ploughing grooves and a secondary layer of laminated wear debris became visible. At 40 and 50 newtons the damage turned aggressive, with massive debris layers and extensive pitting. The team attributes this escalation to rising interfacial temperatures at higher loads, which soften the surface, promote debonding and generate hard debris particles that then scour the interface in a destructive three-body abrasion mechanism. These micrographs directly link the macroscopic wear measurements to observable surface physics.

To optimise the sliding wear process, the researchers turned to Taguchi’s design of experiments, arranging trials in an L25 orthogonal array and using signal-to-noise ratios with a smaller-the-better objective to minimise wear. Analysis of variance on the results showed that normal load was the most influential parameter, contributing 33.33 percent of the variability in specific wear rate, followed by sliding distance at 13.36 percent, reinforcement content at 12.98 percent and sliding velocity at 9.64 percent. The highest F-value, 2.49 for normal load, confirmed its dominant role. The optimal parameter combination produced a signal-to-noise ratio of 58.60 decibels, and a confirmation experiment run at randomly selected settings validated the model with an error of only 3.6 percent, demonstrating that Taguchi’s approach can reliably guide wear-minimising process design for these materials.

Perhaps the most novel element of the study is its use of hybrid multi-criteria decision-making techniques to rank the five composites across all their performance metrics simultaneously. The two-phase AHP-TOPSIS algorithm first converts expert judgment about the relative importance of criteria into quantitative weights using Saaty’s nine-point scale, checking consistency to ensure the weights are trustworthy, and then measures each alternative’s closeness to an ideal solution. The hybrid AHP-R method follows the same first phase but uses reciprocal rank-based weighting in the second. In both analyses, the criteria hierarchy placed hardness, tensile strength, flexural strength and impact strength at the top, with density and wear rate weighted lower, and the consistency ratio of roughly 0.0044 fell far below the accepted 10 percent threshold. Critically, the two independent ranking methods converged on exactly the same order: M6 outperformed M4.5, which beat M3, with M1.5 and M0 trailing, confirming the subjective assessment that the highest marble content is optimal.

The convergence of experimental measurement, statistical optimisation and decision theory gives the findings unusual robustness, and the practical implications are considerable. The authors suggest that composites with low void content and strong mechanical properties are well suited to tribological applications, and that these marble-dust-reinforced aluminium alloys could serve as substitute materials in rollers, brakes, guideways, bearings and gears. Because the reinforcement is essentially industrial waste, the cost and environmental footprint of producing the composites should be far lower than those of conventional ceramic-reinforced alternatives. The work also adds to a growing body of literature showing that hybrid decision-making algorithms such as AHP-TOPSIS and AHP-R, borrowed from operations research, can rapidly and objectively rank material alternatives, sparing engineers from grappling with conflicting criteria by intuition alone.

The study was conducted with support from the Advanced Research Lab for Tribology and the Material Research Centre at Malaviya National Institute of Technology Jaipur, and the authors report no competing interests. While the research remains at the laboratory scale, the combination of a cheap, abundant reinforcement, a scalable casting process and statistically validated performance gains suggests a credible pathway from quarry waste to engineered components. For industries under pressure to cut both costs and carbon, the message of this work is striking: the material of the future for lightweight, wear-resistant metal parts may already be piling up in the dust of India’s marble workshops, waiting to be stirred into the melt.

Subject of Research: Marble dust particle-reinforced AA6061 aluminium matrix composites evaluated for mechanical strength and sliding wear performance using hybrid decision-making techniques

Article Title: Mechanical and sliding wear performance analysis of AA6061 − marble particulates reinforced alloy composites via hybrid decision-making techniques

Article References: Kumar, A., & Kumar, M. (2026). Mechanical and sliding wear performance analysis of AA6061 − marble particulates reinforced alloy composites via hybrid decision-making techniques. Journal of Materials Science: Metallurgy, 1(1), Article 15. https://doi.org/10.1007/s44492-026-00015-z

Image Credits: AI Generated

DOI: 10.1007/s44492-026-00015-z

Keywords: AA6061 alloy, marble dust particulates, metal matrix composites, stir casting, sliding wear, mechanical properties, Taguchi method, ANOVA, hybrid AHP-TOPSIS, AHP-R method, tribology, automotive materials