Structural Strength Analysis and Optimization of Commercial Aircraft Nose Landing Gear under Towing Taxi-Out Conditions Using Finite Element Simulation and Modal Testing
Round 1
Reviewer 1 Report
Comments and Suggestions for AuthorsDear Authors,
Thank you for the opportunity to review this paper. Please find my suggestions.
The paper is analysing the structural response and optimization of aircraft nose landing gear under towing taxi-out conditions, a critical aspect given the operational stresses involved. The integration of finite element simulation with modal testing to validate the mechanical model of the landing gear is particularly noteworthy. The novelty seems to stem from applying a combined approach of simulation and empirical testing to predict and optimize the performance of the landing gear under specific taxiing conditions. This integrated testing/analysis approach allows for a more robust validation of the landing gear's optimization, which is crucial for safety and efficiency in aircraft operations.
Despite the fact that the literature concerning aircraft landing gear systems structural analysis is scarce, there are some additional papers to consider when dealing with this structural analysis and optimization.
1. Yang et al. (2023) describe the use of topology optimization to enhance the design of the main landing gear's lower door, focusing on structural strength, stiffness, and manufacturability (https://iopscience.iop.org/article/10.1088/1742-6596/2557/1/012019)
2. Xue et al. (2012) assess the fatigue life of nose landing gear and implement a structural optimization process using particle swarm optimization to enhance fatigue performance (https://arc.aiaa.org/doi/10.2514/1.C031494)
3. Deng Yangchen (2008) applies shape optimization in the structural design of small aircraft landing gear, using strength and critical loads as constraints to achieve minimum structural weight (https://lxsj.cstam.org.cn/en/article/doi/10.6052/1000-0992-2006-481).
4. Munk et al. (2019) explore the application of topology optimization to solve real-world aerospace design problems, demonstrating the effectiveness of this method in achieving minimum weight structures while complying with aviation industry standards (https://link.springer.com/article/10.1007/s00158-019-02250-6).
Aircraft landing gear systems are critical components tasked with not only supporting the weight of the aircraft during ground operations but also absorbing the substantial impact loads during landing phases.
The paper makes significant contributions to understanding the structural response of aircraft nose landing gear during towing operations. However, addressing the following limitations could enhance the practical value of the research.
1) The paper primarily addresses towing loads but is not comprehensively cover or compare these with the critical landing loads. Given that landing loads are typically more severe and dynamic, the study could benefit from a detailed comparative analysis to contextualize the significance of towing loads within the broader operational load spectrum.
2) The study might be limited by the range of towing speeds and weights considered. Extending this range could provide a more comprehensive understanding of the gear's behavior under extreme and not common loading conditions (edge load cases). Environmental factors such as surface irregularities, weather conditions, and operational practices (like sudden stops or sharp turns during towing) are not clearly addressed.
3) The paper lacks an analysis of the fatigue life of the landing gear materials under repeated towing loads. Long-term durability and the potential for material degradation over time are critical for maintenance and safety considerations.
Author Response
Dear editor and reviewers:
Thank you very much for taking your time to review this manuscript. We appreciate the thoughtful review and constructive feedback provided by the reviewers. We agree with the reviewers' suggestions and will incorporate the recommended changes into the manuscript. Please find my itemized responses in below and my revisions in the re-submitted files.
Reviewers’ Comments to the author:
We are deeply grateful to the editor and reviewers for their valuable suggestions regarding key literature. After meticulously examining the recommended sources, we found them immensely insightful, prompting us to refine our discourse particularly concerning the structural analysis and optimization aspects presented in our paper.
1.The paper primarily addresses towing loads but is not comprehensively cover or compare these with the critical landing loads. Given that landing loads are typically more severe and dynamic, the study could benefit from a detailed comparative analysis to contextualize the significance of towing loads within the broader operational load spectrum.
The author’s answer: Thank you very much for your comments and suggestions concerning our manuscript. The aircraft towing taxi-out departure mode is a novel departure procedure in which the aircraft towing vehicle directly transfers the aircraft from the parking stand to the takeoff runway, enabling a rapid transition. The aircraft towing vehicle does not directly assist in the aircraft’s takeoff and landing, hence mitigating the need to consider impact loads.
- The study might be limited by the range of towing speeds and weights considered. Extending this range could provide a more comprehensive understanding of the gear's behavior under extreme and not common loading conditions (edge load cases). Environmental factors such as surface irregularities, weather conditions, and operational practices (like sudden stops or sharp turns during towing) are not clearly addressed.
The author’s answer: Thank you for this meaningful suggestion. This study represents an initial investigation into the applicability of the aircraft towing taxi-out departure mode, focusing primarily on common behaviors during the towing taxi-out process. Simultaneously, we are in the process of constructing a test stand for real-world experiments, intending to incorporate additional environmental factors and conduct experiments under edge load conditions. However, due to space constraints in this paper and the fact that new research is still in its preliminary stages, further elaboration on these aspects will be undertaken in the next publication.
- The paper lacks an analysis of the fatigue life of the landing gear materials under repeated towing loads. Long-term durability and the potential for material degradation over time are critical for maintenance and safety considerations.
The author’s answer: Thank you for your helpful advice. According to relevant studies, the fatigue life of landing gear primarily depends on the magnitude and variation of dynamic impact loads. The towing taxi-out process is relatively smooth, with relatively small impact loads and variations, thus exerting minimal influence on the structural lifespan. As such, this aspect was not included in the manuscript. However, we intend to verify these conclusions through real-world experiments once the test stand is constructed in the future.
References:
[1] Ma,J.;Xue,C.J.;Deng,Y.Q.;Wang,H. "On Fatigue Life Prediction of a Landing Gear"[J]. Mechanical Science and Technology for Aerospace Engineering,2010,29(01):50-53.DOI:10.13433/j.cnki.1003-8728.2010.01.012.
[2] Wang,M.X. "Analysis of Fatigue Characteristics of a Certain Type Nose Landing Gear"[D]. Nanjing University of Aeronautics and Astronautics.2007.
[3] Chang,Q.C. "Research on Fatigue Reliability and Functional Reliability with Interrelated Multiple Failure Modes of Landing Gear Steering Mechanism"[D]. Nanjing University of Aeronautics and Astronautics.2019.
Author Response File: Author Response.DOC
Reviewer 2 Report
Comments and Suggestions for AuthorsDear authors,
please, see the attached file with my comments
regards
Note: improve the description of the numerical analyses performed, especially regarding the constraint conditions considered
Comments for author File: 
Comments.pdf
Author Response
Dear editor and reviewers:
Thank you very much for taking your time to review this manuscript. We appreciate the thoughtful review and constructive feedback provided by the reviewers. We agree with the reviewers' suggestions and will incorporate the recommended changes into the manuscript. Please find my itemized responses in below and my revisions in the re-submitted files.
Reviewers’ Comments to the author:
We are deeply grateful to the editor and reviewers for their valuable suggestions regarding key literature. After meticulously examining the recommended sources, we found them immensely insightful, prompting us to refine our discourse particularly concerning the structural analysis and optimization aspects presented in our paper.
- Introduction
Line 107: testing28 … ?
The author’s answer: Thanks. This is a reference to source number 28, which has been formatted correctly according to the reference style (line 108).
- Model Verification
Lines 116: the dynamic control equation … the homogenous equation
Eq. (1) … remove the curly braces
Eq. (4) … φi must be a vector …
Lines 160: Software used to prepare the FE model ? Number of nodes ? Number of
elements ? Type of elements … linear ? parabolic ? …
Lines 162: Figure 4 does not show the material …
Figure 6: It seems to me that modes 5, 6 and 7 are also bending modes …
Figure 6 and Table 1: How is the FE model constrained ?
Figure 7 … Well done !
Figure 9: this figure is not mentioned in the text … please separate the images
Are the wheels in contact with the ground during the test? or is the gear suspended, i.e.
detached from the ground? … Please clarify.
Line 226 … briefly explain how the modal analysis software was used. Is it internally
developed software? is it commercial software? How, in practice, are the natural
frequencies of the system identified?
Line 241 … constraint conditions? … Do they represent the operating conditions of the
gear during taxiing manoeuvres?
Eq. (6) … ??? … static load ?
The author’s answer: Thank you for this meaningful suggestion. The matrices and vectors in the formulae previously found problematic have been corrected to their accurate forms (Eq. (1-6)). To enhance the precision of the description concerning finite element analysis settings, images depicting elements, nodes, materials, and boundary conditions have been added (Fig.4). Observing modal deformations from the first to the fourth and fifth to the seventh modes in Figure 6, a comparison with the pre-deformation images in gray reveals distinct differences. The former's deformation occurs on either the XOZ or YOZ plane alone, while the latter, due to twisting, shows deformation on both the XOZ and YOZ planes. Additionally, since the mid to lower section of the damping strut is cylindrical, the twisting can only be identified by examining the deformation characteristics. Figure 9 is also mentioned within the text (line 219). During testing, the aircraft is positioned on the airport apron with its wheels directly contacting the ground. The DASP software mentioned in this paper is a Chinese-developed modal analysis software known for its high degree of automation in modal identification. The ERA method used is widely applied in structural analysis in the aerospace sector, quickly and accurately determining the natural frequencies of structures. This text has been revised for clearer expression (line 229-236). The subsequent text simplifies the analysis of the front landing gear, where the static load analysis conducted aims to solve for the structure's stiffness.
- Dynamic Simulation
Figure (14) … What are the degrees of freedom?
the models represented in Figure (14) and Figure (15) are two different things ... explain
better what was done ...
Figure (16) … These results were obtained with which numerical model?
Lines 313 and 314 … It seems to me that the results are practically the same regardless of
speed
Figure (18) … It's not clear how the gear strut actually deforms ... it would be better to
plot the x, y and z displacement components separately … How is the model constrained?
It is not understandable ..
The author’s answer: Thank you for your helpful advice. In Figure 14, this paper simplifies the model of towing taxi-out into two degrees of freedom for the aircraft tug's wheels, one degree of freedom for the wheel-engaging mechanism with the wheel, and one degree of freedom for the vertical vibration of the front landing gear. In the subsequent dynamic simulation process, this simplification is extended into three-dimensional space, allowing every factor affecting the vertical vibration of the front landing gear to be considered. We use ADAMS software to simulate towing departures, which can directly output the vertical force data on the front landing gear. Therefore, data from various working conditions are exported and compared in Figure 16. You are right, under this departure mode, the towing system's speed generally does not exceed 50 km/h, which is relatively low-speed. Our studies have also found that speed has a minor impact on the front landing gear in this new departure mode. Our main objective is to verify the response of the front landing gear under different conditions, with speed being a significant parameter for our research. To facilitate observation of the deformation of the front landing gear in various directions during towing taxi-out, stress cloud maps in the x, y, and z directions have been added to illustrate (Fig.18).
- Structure Optimization
Line 335 and Line 355 … geometric modelling software … which software ?
Figure 23 (a) and Figure 23 (b) … are unreadable !!!
Line 368 … all deformations did not lead to structural failure … what does it mean ... you
haven't carried out a real structural check, they are just deformation calculations ... your
conclusions are not fully demonstrated
The author’s answer: Thank you very much for your comments and suggestions concerning our manuscript. The text indicates that the model drawing software used is CATIA (line 342); adjustments have also been made to the size and clarity of certain images to facilitate reading (Fig.17, Fig.23). This article primarily conducts a theoretical analysis under the towing taxi-out mode based on a model validated by experiments. It concludes that no structural damage occurred during the simulation, providing support for subsequent experiments. We are currently setting up a real aircraft test rig, which will soon conduct a real-world test of the front landing gear strength of a B-727 aircraft in towing taxi-out mode, serving as a solid validation of the theoretical analysis presented in this paper.
Author Response File: Author Response.DOC
