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

Ren, Kaitao; Ren, Zhigui; Zhang, Heng; Zhang, Yijian; Chen, Yuxiang; Liu, Ruibo

doi:10.5194/ms-2026-167

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https://doi.org/10.5194/ms-2026-167

Preprints

07 Sep 2026

| 07 Sep 2026

Status: this preprint is currently under review for the journal MS.

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

Kaitao Ren, Zhigui Ren, Heng Zhang, Yijian Zhang, Yuxiang Chen, and Ruibo Liu

Abstract. During dense hard-soil excavation, the stick sustains large digging resistance, and long-term static and cyclic impact loads frequently cause failure of critical structural components. Balancing structural performance and digging capacity remains a core bottleneck in excavator attachment design. Using a 20-ton hydraulic excavator as the research prototype, this study proposes a Structure-Mechanism Collaborative Optimization (CO) approach that explicitly accounts for the coupling between mechanism parameters and structural performance. A multidisciplinary CO model was constructed, in which stick digging force and equivalent von Mises stress were calculated from experimental data and critical dangerous conditions were identified from stress distributions. Optimal Latin Hypercube Design (OLHD) combined with Kriging surrogate models was employed to build three surrogate models for digging force, maximum equivalent stress, and stick mass, substantially reducing computational cost. The CO model was subsequently solved by intelligent optimization algorithms under practical engineering constraints. Results demonstrate a 9 % increase in theoretical digging force, a 7 % reduction in maximum equivalent stress, and a 9 % decrease in stick weight.

Received: 03 Sep 2026 – Discussion started: 07 Sep 2026

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Kaitao Ren, Zhigui Ren, Heng Zhang, Yijian Zhang, Yuxiang Chen, and Ruibo Liu

Status: final response (author comments only)

RC1:
'Comment on ms-2026-167', Anonymous Referee #1, 12 Sep 2026

This paper tries to offer a mechanism‑structure collaborative optimization design method of excavator stick under hard‑soil conditions . However, here are some suggestions：
1.How do you ensure the accuracy of the simulated results?
2.How do you determine the weight coefficient for the three optimization objectives?
3. What is your novelty?
4. English writing could be improved.

Citation: https://doi.org/10.5194/ms-2026-167-RC1
- CC1:
  'Reply on RC1', Zhigui Ren, 14 Sep 2026
  You may be the reviewer of this manuscript before its resubmission. Previously, I have revised the paper framework according to your comments. I sincerely appreciate your valuable suggestions raised in this round. The manuscript will be comprehensively improved in accordance with your remarks. Below are our preliminary responses to the questions you put forward above.
  In Section 5 on optimization results, the optimized variables are substituted into the digging force calculation and stress simulation models proposed and validated by our group (Ref. 26). Error analysis is performed between the surrogate-model predicted objectives and recalculated values, and the errors are within an acceptable range, verifying the accuracy of the optimization model.Unfortunately, our group has limited funding to carry out physical experiments for further validation. The verification strategy was not clearly elaborated in the original manuscript, which may have led to this misunderstanding. We will supplement and refine this description thoroughly in the revised paper.The original text is as follows: The re-calculated values of digging force, maximum equivalent stress, and stick weight were then compared against the surrogate model predictions. The re-analysis results show that the deviations between surrogate predictions and FEA verification values are 1.368% for digging force, 1.144% for maximum equivalent stress, and 1.414% for stick weight, all remaining within 1.5%. These small discrepancies confirm that the constructed Kriging surrogate models possess sufficient approximation accuracy, and that the collaborative optimization results are physically reliable and engineering-applicable.
  
  In this work, empirical weighting combined with comparative‑analysis of multiple weight combinations is adopted to determine the weight coefficients. For compacted hard‑soil excavation conditions of hydraulic excavators, improving digging capacity and guaranteeing structural safety are the primary design requirements, whereas lightweight design is a secondary objective. Therefore, higher weights are assigned to digging force and maximum equivalent stress, and a relatively lower weight is assigned to stick mass.If revision is permitted, we will re-describe the determination of weight coefficients to make this part more scientific and comprehensive.
  
  A mechanism‑structure multidisciplinary collaborative optimization model considering cosine‑distributed hinge‑bore loading is established. Most existing studies optimize mechanism parameters or structural plate thickness separately and ignore their mutual coupling effect. In this paper, both hinge‑point geometric parameters and structural plate‑thickness variables are incorporated within a two‑level Collaborative Optimization (CO) framework. The cosine‑distributed load scheme is adopted to reproduce realistic pin‑hole contact and avoid spurious stress concentration caused by point loads. Synchronous optimization for digging capacity, structural stress and stick mass is realized.
  
  We appreciate your valuable comments. We have comprehensively polished the full manuscript, rephrased awkward and redundant sentences, and standardized all technical terms.
  
  Thank you again for your valuable comments. We will carefully revise and supplement the manuscript to address all the above issues. If we are granted the opportunity for revision, we will submit the revised manuscript for your consideration. We appreciate your time spent reviewing our work.
  
  Citation: https://doi.org/10.5194/ms-2026-167-CC1
- AC2:
  'Reply on RC1', Kaitao Ren, 20 Oct 2026
  We sincerely thank the reviewer for the careful evaluation and constructive suggestions, which help us greatly improve the quality of this manuscript.Below is our preliminary response to your questions. We will carefully address all the raised points in the revised manuscript to further improve the novelty and completeness of this work.
  In Section 5 (Optimization Results), the optimized design variables are substituted into the digging force calculation and stress simulation models developed and validated by our research group (Ref. 26). We conduct an error comparison between the objective values predicted by the surrogate model and those recalculated via the high-fidelity models. The resulting errors fall within an acceptable range, which supports the validity of the established optimization framework. We fully recognize that the validation strategy was not sufficiently clarified in the original manuscript, which may have caused confusion. Owing to budget constraints within our group, physical prototype tests for further experimental verification are currently unavailable. We will add detailed, systematic descriptions of this verification logic in the revised version to avoid such ambiguity.The relevant original passage reads: The re-calculated values of digging force, maximum equivalent stress, and stick weight were then compared against the surrogate model predictions. The re-analysis results show that the deviations between surrogate predictions and FEA verification values are 1.368% for digging force, 1.144% for maximum equivalent stress, and 1.414% for stick weight, all remaining within 1.5%. These small discrepancies confirm that the constructed Kriging surrogate models possess sufficient approximation accuracy, and that the collaborative optimization results are physically reliable and engineering-applicable.We will further refine the description of weight coefficient selection to improve its rationality and comprehensiveness.
  
  In the present study, weight coefficients are determined by combining empirical assignment with comparative analysis of multiple weight combinations. For compacted hard-soil excavation scenarios of hydraulic excavators, enhancing digging performance and ensuring structural safety represent the priority design targets, while lightweight design serves as a secondary objective. Accordingly, relatively larger weights are allocated to digging force and maximum equivalent stress, and a smaller weight is set for stick mass. We will further revise the description regarding the selection of weight coefficients to strengthen its rationality and comprehensiveness.
  
  We agree that the description of novelty in the original manuscript is not sufficiently precise. The core contribution of this work is not merely the application of the collaborative optimization framework. The main novelties are as follows. During excavation in compacted hard soil, the bucket bears considerable excavation resistance. Longterm static and cyclic impact loads frequently induce failure of key structural components. Balancing structural performance and digging capacity remains a critical bottleneck in the design of excavator attachments. Taking a 20ton hydraulic excavator as the research prototype, this paper proposes a mechanismstructure Collaborative Optimization (CO) method to handle the coupling between mechanism geometric parameters and structural dimension parameters, so as to simultaneously improve structural strength and working performance.
  
  We sincerely appreciate your constructive remarks. We have carefully revised the entire manuscript, rewording cumbersome and less concise expressions throughout the text.
  
  Citation: https://doi.org/10.5194/ms-2026-167-AC2
RC2:
'Comment on ms-2026-167', Anonymous Referee #2, 04 Oct 2026
The optimized values in Table 5 are inconsistent with the variable constraints in Table 3. For example, x_k₁ is constrained to 2769–3061 mm, whereas the optimized value is 2276.60 mm. The feasibility and consistency of the optimization results should therefore be verified.

The selection of the 1 m excavation condition is insufficiently justified. No quantitative criterion or comparative analysis is provided to demonstrate that it represents the most critical working condition.

Only 300 samples are used despite the relatively large number of design variables. A sample-size sensitivity analysis is recommended to demonstrate that 300 samples are sufficient for reliable surrogate-model training and design-space representation.

The manuscript emphasizes long-term static and cyclic impact loads, but the optimization considers only the maximum von Mises stress. Fatigue-related indicators are absent, and the basis for the allowable stress of 230 MPa should also be clarified.

The criterion for selecting the final compromise optimal solution is unclear. The authors should provide the decision-making method and justification for the selected solution.

The novelty of the study should be stated more clearly. The authors should clarify whether the contribution lies in the organization of design variables, the mechanism–structure coupling strategy, or the optimization method, rather than simply presenting the use of CO as the main innovation.

There are unit errors in the tables. The material strength unit in Table 1 and the mass unit in Table 4 should be corrected.

8. Several inconsistencies exist in the mathematical descriptions. For example, “In Equation (1)” is used when discussing Equation (2), and some variable definitions do not match the corresponding symbols. The equations and notation should be carefully checked.
Citation: https://doi.org/10.5194/ms-2026-167-RC2
- AC1:
  'Reply on RC2', Kaitao Ren, 20 Oct 2026
  We sincerely appreciate your time and all valuable constructive comments on our manuscript. Your suggestions are of great significance for improving the quality of this work. Below are our pointbypoint preliminary responses to your concerns.
  Thank you for your careful checking. This inconsistency does not indicate invalid optimization results; it originates from a typesetting and entry error in Table 5 of the original manuscript. The true optimized value of x_k1falls within the constraint range of 2769–3061 mm. This mistake will be corrected in the revised manuscript.
  
  We agree with this comment and appreciate your suggestion. The original manuscript lacked sufficient explanation for selecting the 1 m excavation depth as the target working condition. The excavation trajectory at 1 m depth has a relatively short stroke. During the initial cutting stage, the bucket rapidly penetrates compacted hard soil, concentrating resistance loads and producing obvious impact effects. Therefore, the 1 m condition is selected for subsequent analysis. We will supplement this explanation in the revised manuscript.
  
  Thank you for this valuable suggestion, which is very important to this work. We will add a samplesize sensitivity analysis in the revised version to demonstrate that the current sample size is sufficient to train a reliable surrogate model.
  
  This is a crucial comment. The present optimization targets structural strength evaluation under ultimate impact loads, and fatigue analysis will be carried out in our followup extended research. The allowable stress of 230 MPa is calculated from the yield strength of Q345 steel with a safety factor of 1.5: the yield strength of Q345 is 345 MPa, so the allowable stress[σ]=345/1.5=230MPa.
  
  We appreciate the reviewer for pointing out this deficiency. In this study, the TOPSIS multicriteria decisionmaking method is adopted to select the compromise optimal solution from the Pareto optimal set. Each objective function is normalized, and the closeness coefficient of each Pareto solution is calculated. The solution with the highest closeness coefficient is selected as the final compromise solution to balance structural stress and mechanism performance. We will add descriptions about this decisionmaking method and the selection rationale in the revised manuscript.
  
  We agree that the description of novelty in the original manuscript is not sufficiently precise. The core contribution of this work is not merely the application of the collaborative optimization framework. The main novelties are as follows. During excavation in compacted hard soil, the bucket bears considerable excavation resistance. Longterm static and cyclic impact loads frequently induce failure of key structural components. Balancing structural performance and digging capacity remains a critical bottleneck in the design of excavator attachments. Taking a 20ton hydraulic excavator as the research prototype, this paper proposes a mechanismstructure Collaborative Optimization (CO) method to handle the coupling between mechanism geometric parameters and structural dimension parameters, so as to simultaneously improve structural strength and working performance.
  
  We sincerely apologize for these careless unit errors. We have rechecked all tables throughout the manuscript and corrected the unit mistakes for material strength in Table 1 and mass in Table 4.
  
  Thank you for your careful proofreading. We have thoroughly checked all equations, crossreferences of equation numbers, variable symbols and their definitions throughout the manuscript. The mistake where Equation (2) was mistakenly cited as Equation (1) in the discussion has been corrected. All variable definitions are consistent with formula symbols, and these issues have been resolved in the revised version.
  
  Citation: https://doi.org/10.5194/ms-2026-167-AC1

Kaitao Ren, Zhigui Ren, Heng Zhang, Yijian Zhang, Yuxiang Chen, and Ruibo Liu

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Short summary

Aiming at stick failures under hard‑soil excavation, this paper presents a mechanism‑structure collaborative optimization for a 20‑ton excavator. With test‑identified hazardous conditions and Kriging surrogate models, NSGA‑II‑based two‑level optimization boosts digging force by 9 %, cuts peak stress by 7 % and reduces stick weight by 9 %. It provides references for excavator‑attachment multidisciplinary optimization.


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