Meccanica最新文献

The following paper focuses on structural displacement tracking that is a significant process, inter alia, for evaluating safety of structures, load classification, or structural control applications. The authors presented a method for the full-field displacement identification based on strain sensor measurements and machine learning. Using this method, it is possible to recreate full-field displacement maps of the entire structure or its parts, even for different load cases. An example is given in which a typical aerostructure (composite hat-stiffened panel) is subjected to displacement monitoring. Two neural networks were trained to identify full-field displacement maps of the panel, based on strain gauges measurements. The accuracy of the predictions was experimentally tested using digital image correlation (DIC). The predicted displacement maps were qualitatively and quantitively compared with the results of finite element simulation and experimental DIC measurements.

Gvirtzman et al. (Nature 637(8045):369–374, 2025) have made recently very interesting experiments showing how small shear cracks nucleate and then evolve at the interface between two rectangular blocks. They find essentially an approximate geometrical factor for confined cracks in plates in the condition for nucleation (threshold shear stress (tau _{thresh})) in a classical Griffith crack condition for quasi-static nucleation. However, they seem to suggest that slowly creeping patches approach the interface width and accelerate only when a topological transition takes place in which they become 1D through cracks. We observe that this second implication is due to the fact that the measured threshold shear stress (tau _{thresh}) is very close to the cohesive strength (tau _{coh}) in previously reported experiments by the same group in PMMA solids (about 1 MPa), which suggests the width of the specimen they have used may be rather special. The general model they have derived is entirely consistent with classical fracture mechanics, which doesn’t require cracks to accelerate at this topological change. Including the cohesive strength (tau _{coh}) crack nucleation in the model, and how cracks should behave when they are very small with respect to the plate width W, we provide a possible diagram of nucleation of cracks, depending on their shape and dimension, showing that we should take care when using their new formula, because deviations may be large if cracks are small—a full 3D numerical solution is to be preferred which is not difficult to obtain today.

The dynamics of a hanging chain pendulum, long treated as a textbook problem in classical mechanics, are revisited from a fresh and rigorous analytical perspective. By systematically deriving and comparing the continuum and discrete formulations, subtle but significant differences in the vibrational spectrum, particularly in the high-frequency regime are uncovered. Using asymptotic expansions, boundary layer theory, and matched scaling arguments, a comprehensive description of the eigenmodes and their scaling behavior is developed. In the discrete model, we reveal a striking two-regime structure: low-frequency modes governed by Bessel-type equations, and high-frequency modes localized near the free end, described by Airy-type asymptotics. The transition between these regimes emerges naturally from a balance of competing terms in the governing equations, yielding a characteristic crossover scaling. This analysis clarifies the limitations of discrete and continuum approximations and exposes the deeper mathematical structure underlying the system. Ultimately, the followed approach provides a dual perspective and case study, demonstrating how rigorous asymptotics bridge discrete and continuum models and yield fresh insight into seemingly well-understood mechanics of the chain pendulum.

A new method based on Berkovich nanoindentation is proposed to predict the stress–strain curve of hardened martensitic bearing steels. This method combines a theory for predicting yield strength with experimental Berkovich indentation. Kick’s constant has been identified as the most robust parameter derived from sharp nanoindentation tests. The yield limit is predicted using a screw-dislocation strengthening theory, while the steel hardening exponent is calculated using Kick’s constant derived from the nanoindentation data. This ’hybrid method’ shows good agreement with experimentally measured stress–strain curves of different bearing steels, combining the strengths of both experimental and theoretical approaches. The proposed model elegantly addresses the long-standing challenge of deriving a unique solution for the material stress–strain curve from nanoindentation test data.

This paper investigates the nonlinear transient dynamics of pneumatic tyres by extending the recently introduced two-regime modelling framework. Unlike classical single-contact-point models, which describe force generation via first-order relaxation dynamics, the two-regime approach directly models the evolution of tyre forces and aligning moment through a set of nonlinear ordinary differential equations derived from the underlying brush-type partial differential equations. A key contribution of this work is a general recursive methodology, based on the implicit function theorem, for reconstructing the slip surfaces from any analytical steady-state tyre model, including non-invertible formulations such as Pacejka’s Magic Formula. The stability properties of the proposed models are analysed, revealing the crucial role of the slip stiffness matrix in determining singular behaviours and transient instabilities. Simulations are conducted using an isotropic Magic Formula model for combined slips, demonstrating significant dynamical differences between the two-regime and single-contact-point formulations, including non-minimum phase effects and velocity-dependent relaxation phenomena. The results establish a direct connection between the steady-state and transient tyre characteristics, providing new insights into the nonlinear dynamics of rolling contact systems.

This paper proposes a novel decoupling algorithm with an error auto-compensation strategy for general six-axis acceleration sensing mechanisms. First, mathematical preliminaries on vectors, matrices and quaternions are given. Then, dynamic equations are derived according to Kane’s equations and solved numerically using the trapezoid formula. To improve the accuracy of the solution, an auto-compensation strategy based on the vibration properties is introduced. Additionally, the compensation conditions of this strategy are determined through error characteristic analysis. Subsequently, virtual prototype experiments are conducted to verify the performances of the proposed algorithm. The results indicate that: (1) under 5% interference noise, the proposed algorithm performs effectively across all chosen configurations (“6–6”, “9–3”, “9–4”, “12–4” and “12–6”), with comprehensive relative errors reduced by up to 54.15%; (2) it takes the proposed algorithm only 0.13 s to process data spanning 3 s, with a comprehensive relative error of 0.03%; (3) despite the varying interference noise, the comprehensive relative error remains within 1.06%. Finally, the actual prototype experiment further demonstrates the feasibility of the proposed decoupling algorithm, with a maximum comprehensive relative error of 5.82%.

As a continuation of Part 1’s numerical simulation, this paper presents a comprehensive experimental study of an end-sealed squeeze film damper (SFD). Three overlapping buckle piston rings with opening gaps of 40 mm, 50 mm, and 60 mm, with their flow conductances quantified through static leakage tests. Dynamic excitation experiments by single frequency are conducted under varying oil supply pressures (1.0, 3.0, and 4.0 barG) to evaluate inertia and damping coefficients. Results show that both higher supply pressure and larger opening gaps increase the dynamic coefficients. These measurements show good agreement with the predictions using the numerical model developed in Part 1, further validating the model’s applicability. A full‐sized rotor test rig incorporating an end-sealed SFD, with a total rotor mass of 640 kg, is developed based on an aero-engine, assembling piston rings with a 60 mm opening gap. The SFD’s ability to suppress lateral vibration as the rotor crosses the first-order critical speed is assessed under three unbalances (3022.5 g mm/0 deg, 6254 g mm/190 deg, and their combinations), and the effect of oil supply pressure on vibration amplitude is also investigated. The results confirm that the end-sealed SFD significantly dissipates rotor vibration energy, providing excellent vibration suppression, not limited to the resonance response, with a maximum amplitude reduction of 71.7%. These findings highlight the importance of co-optimizing rotor unbalance, piston ring’s opening gap, and oil supply pressure for effective SFD design.

This article explores the implementation of elliptical pins in cycloidal pin gear transmissions, a modification aimed at enhancing their performance characteristics. Traditional cycloidal drives utilize circular pins, but this study investigates the potential benefits of using elliptical pins, including reduced contact stress and improved lifespan of the transmission components. A new calculation method is proposed for determining the profile, curvature, forces, and stresses in both epicycloidal and hypocycloidal gears with elliptical pins. This method was used to optimize parameters of an example gear. The study demonstrates that elliptical pins can reduce the equivalent curvature and contact stress in the transmission. This reduction of stress is small (up to 13% for gears in the paper), but it should not be neglected as it can significantly increase the lifespan of the transmission. Finite element analysis showed that the reduction can be even greater. Also, the occurrence of undercutting in hypocycloidal gears was investigated. Additionally, the design of the prototype of a 2K-V epicycloidal reducer with elliptical pins suitable for 3D printing, is considered.

Compliant joints are widely used in precision positioning stages due to their nearly zero friction. A two-dimensional rigid-flexible coupling positioning stage (2D-RFCPS) containing multiple compliant joints is proposed to compensate for positioning errors caused by nonlinear friction, achieving long-stroke ultra-precision positioning. The kinetic and strain energies of the moving stages in the 2D-RFCPS are calculated based on the floating frame approach and the finite element method, respectively. These are used to establish the dynamic model of the 2D-RFCPS using the Lagrangian equation, revealing vibration coupling effects between the moving stages across six spatial directions. The accuracy of the dynamic model is validated through two comparative experiments. First, simulations under constant and harmonic forces are conducted using MATLAB and ADAMS, with the maximum root-mean-square error (RMSE) between the MATLAB and ADAMS results in displacement and velocity are 6.86E-4m and 2.9E-3m/s, respectively. Second, active disturbance rejection control (ADRC) algorithm is applied for point-to-point motion simulations and physical experiments, resulting in RMSE values of 8.80E-6m and 1.74E-4m/s in displacement and velocity, respectively. Additionally, the effectiveness of the dynamic model is demonstrated through vibration coupling analysis between the X-Tab and Y-Tab across six spatial directions. Notably, the Y-Tab rotation around the Z-axis is significantly influenced by the eccentric inertial torque, with the rotation amplitude increasing by 177.7% at the eccentric position.

Inspection and maintenance of large structures, such as ship hulls and oil tanks, are essential for ensuring safety and operational efficiency. Traditional manual inspection methods are often labor-intensive, time-consuming, and potentially hazardous. This study proposes a novel solution: a lizard-inspired quadruped wall-climbing robot (LQWCR). Inspired by the morphology and locomotion of lizards, the robot’s leg design, kinematics, and dynamics are systematically analyzed. To facilitate control, the system dynamics are linearized using a Back Propagation (BP) neural network model. Based on this model, innovative motion control strategies are developed to achieve precise trajectory tracking. Additionally, compliance control strategies are introduced to mitigate impact forces when the robot’s foot interacts with welds, improving its adaptability to unstructured environments. Simulation results demonstrate that these strategies effectively enable the robot to negotiate weld seams and reduce the risk of falling. This research lays a theoretical foundation and provides technical support for applying wall-climbing robots to inspection, maintenance, and surveillance tasks in real-world scenarios.