The study, led by Kaitao Ren and corresponding author Zhigui Ren, introduces what the authors call a Structure-Mechanism Collaborative Optimization approach for the stick of a 20-ton hydraulic excavator. The central insight is that mechanism parameters—the geometry of hinge points and linkage dimensions that govern how hydraulic cylinders convert their motion into digging force—and structural parameters such as plate thicknesses are deeply coupled. Most previous studies have optimized these two aspects separately, adjusting either the linkage geometry or the steel plate gauges without accounting for how a change in one domain alters the loads and stresses in the other. By explicitly modeling that coupling, the team argues, designers can find solutions that neither approach could reach alone.

The researchers began with physical evidence rather than pure simulation. Using experimental data from the machine, they calculated the stick’s digging force and the equivalent von Mises stress—a standard measure that combines the multi-directional stress state at a point into a single comparable value—across the working envelope. From the measured stress distributions they identified the critical dangerous conditions, the specific postures and load cases in which the stick is most at risk of failure. Anchoring the optimization in test-identified hazardous conditions is a key methodological choice, because it ensures the design effort targets the scenarios that actually break hardware in the field rather than idealized load cases that rarely occur.

With those conditions established, the team confronted a familiar computational bottleneck. Evaluating digging force and stress across the full design space of hinge geometries and plate thicknesses would require thousands of finite element analyses, each computationally expensive. Their solution was to combine Optimal Latin Hypercube Design, a sampling strategy that spreads test points efficiently across a multi-dimensional space, with Kriging surrogate models—a class of statistical interpolators, originally developed in geostatistics, that can approximate the output of expensive simulations with quantified accuracy. Three surrogate models were built, one each for digging force, maximum equivalent stress, and stick mass, allowing the optimization algorithms to explore the design space at a fraction of the computational cost of repeated full simulations.

The optimization itself was organized as a two-level Collaborative Optimization model, a multidisciplinary design framework in which individual disciplines are optimized in parallel under coordination from a system-level optimizer, with consistency among the disciplines enforced through shared targets. The model was solved using intelligent optimization algorithms, including NSGA-II, a widely used evolutionary algorithm well suited to problems with multiple competing objectives, under practical engineering constraints. The objectives pull in different directions: more digging force generally means heavier structure or higher stress, while reducing weight tends to raise stress levels. The team weighted the objectives empirically, assigning higher priority to digging capacity and structural safety—regarded as the primary requirements for hard-soil excavation—and a lower weight to mass reduction as a secondary goal.

The reported results are striking in their balance. The optimized design increases theoretical digging force by 9 percent, reduces the maximum equivalent stress in the stick by 7 percent, and cuts the stick’s weight by 9 percent. Achieving all three simultaneously is the noteworthy part: typically, a designer must trade one against another. A stronger, lighter arm that is also less stressed represents a genuine Pareto improvement, meaning the collaborative optimization found a design that dominates the baseline on every metric considered. For manufacturers, a 9 percent weight reduction translates directly into material savings and reduced machine mass, while the stress reduction promises longer component life under the cyclic loading that defines hard-soil work.

Verification of the surrogate-based results was addressed through recalculation. When the optimized design variables were substituted back into the digging force calculation and stress simulation models previously developed and validated by the research group, the deviations between surrogate predictions and the finite element verification values were 1.368 percent for digging force, 1.144 percent for maximum equivalent stress, and 1.414 percent for stick weight—all within 1.5 percent. According to the authors, these small discrepancies confirm that the Kriging surrogate models possess sufficient approximation accuracy and that the collaborative optimization results are physically reliable and applicable in engineering practice. The team has acknowledged that limited funding prevented further physical experimental validation at this stage, a point they intend to elaborate more clearly in the revised manuscript.

One technical detail deserves attention from anyone who has modeled pinned machine structures: the load scheme. Rather than applying idealized point loads at the hinge bores, which are known to produce spurious stress concentrations that do not exist in real pin connections, the researchers adopted a cosine-distributed loading scheme to reproduce realistic pin-hole contact conditions. This choice matters because an optimizer driven by artificial stress peaks will make bad decisions—thickening plates in the wrong places or distorting geometry to relieve stresses that would never occur in service. By distributing the load realistically across the bearing surface of each hinge bore, the model keeps the stress predictions meaningful for the actual contact mechanics of a pinned joint.

The work is a preprint, released on 7 September 2026 and open for community discussion until 18 October 2026, and referees have already raised substantive questions that will shape the final version. Among the issues flagged are the consistency of some optimized variable values with their stated constraints, the justification for selecting the 1-meter excavation condition as representative of the most critical case, the sufficiency of 300 training samples for the surrogate models given the number of design variables, and the absence of fatigue-related indicators even though the paper emphasizes long-term cyclic impact loading. The authors have responded constructively, noting that empirical weighting combined with comparative analysis of multiple weight combinations was used, and that the manuscript will be comprehensively revised in response to the comments.

Even in preprint form, the study offers a template for how heavy equipment design may evolve. Excavator attachments sit at the intersection of kinematics, hydraulics, and structural mechanics, and the failure modes that matter—fatigue cracks initiating at welded hinge lugs, buckling under peak resistance, excessive deflection—depend on all three domains at once. The collaborative optimization framework demonstrated here, pairing test-identified load cases with surrogate-accelerated multi-objective search, provides a reference workflow that other attachment designers can adapt, whether for buckets, booms, or the arms of loaders and backhoes. As computational tools mature and surrogate modeling becomes routine, the era of optimizing one discipline at a time may be drawing to a close, replaced by designs in which mechanism and structure are tuned together from the start.

Subject of Research: Mechanism-structure collaborative optimization of an excavator stick for hard-soil digging conditions

Article Title: Mechanism‑Structure Collaborative Optimization Design of Excavator Stick under Hard‑Soil Conditions

Article References: Ren, K., Ren, Z., Zhang, H., Zhang, Y., Chen, Y., & Liu, R. (2026). Mechanism‑Structure Collaborative Optimization Design of Excavator Stick under Hard‑Soil Conditions. https://doi.org/10.5194/ms-2026-167

Image Credits: AI Generated

DOI: 10.5194/ms-2026-167

Keywords: excavator, stick, collaborative optimization, Kriging surrogate model, NSGA-II, von Mises stress, hard soil, multidisciplinary design optimization, structural lightweighting, digging force, finite element analysis, Mechanical Sciences