Meccanica最新文献

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.

This study introduces a geometrically nonlinear electromagnetic energy harvester employing symmetrical inclined springs. Precise adjustment of vertical spring spacing enables controlled configuration of either bistable or tristable potential wells and their depths. Global dynamic analysis of this energy harvesting system (combining extended averaging, Runge–Kutta, and cell-mapping methods) reveals resonant characteristics, potential-well transitions, and the evolution of basins of attraction (BAs) under harmonic base vibration. It is found that the tristable system enables voltage generation under ultra-weak vibrations near trivial equilibrium. By comparison, the bistable system achieves high-energy orbits with lower activation thresholds for high-energy intra-/inter-well states and sustains high-voltage output across a wider effective bandwidth. High-energy attractors demonstrate extreme sensitivity to initial states due to fractal basin boundaries, leading to unpredictable collapses to low-energy states that critically compromise reliability. The bistable configuration exhibits superior robustness across medium-to-high vibration amplitudes, attributed to its larger and contiguous BAs supporting high-output responses, which counters claims of tristable peak-voltage superiority under extreme base vibrations. These results provide theoretical support for guiding reliable optimization of geometrically nonlinear energy harvesters in low-frequency vibration environments.

This study investigates the size-dependent eigen-buckling behavior of Kirchhoff microplates within the framework of a modified strain gradient theory (MSGT), which introduces three intrinsic material length scale parameters and leads to a sixth-order governing differential equation. Using the variational principle, both classical and non-classical boundary conditions are systematically derived in a concise form. The direct separation of variables method is extended to solve the eigenvalue problem arising from the MSGT model. In particular, for configurations where two adjacent edges are clamped and the remaining edges are either clamped or simply supported, closed-form analytical solutions which have previously been considered unattainable are achieved for the first time. A comprehensive parametric study is performed to examine the influence of various boundary conditions and material length scale parameters on the critical buckling loads, thereby elucidating the inherent size-dependent stability behavior at micro- and nano-scales. These results provide critical insights into the eigen-buckling characteristics of Kirchhoff microplates and further contribute to the theoretical foundation for the design and analysis of micro-/nano-scale systems.

The introduction of the Delta parallel robot and the SCARA serial manipulator marked a significant milestone in the evolution of industrial robotics. Since then, there has been a growing wave of innovative proposals for robots capable of executing Schönflies motion. Parallel manipulators with identical limbs have played a crucial role in shaping these robotic topologies. However, maintaining symmetry presents crucial challenges, particularly due to the complexity of mechanical assembly and the high precision required in manufacturing. This work explores the kinematics of an innovative Schönflies-motion parallel manipulator through the application of screw theory, an algebraic framework with profound geometric significance. The manipulator is composed of serial kinematic chains with two distinct degrees of freedom. While this design compromises symmetry, it significantly streamlines both kinematic analysis and overall construction. By eliminating passive kinematic chains, it offers a practical alternative to traditional parallel manipulators constructed from closed kinematic chains incorporating parallelogram-type linkages. To ensure the reliability of the proposed kinematic analysis method, numerical validation is performed using an alternative approach: an algorithm based on numerical data fitting.

This study presents a novel and efficient modal analysis framework for thick cylindrical structures with complex geometry and material variability, subject to arbitrary boundary conditions. The methodology is applied to an electric motor (e-motor) stator assembly modelled as a thick cylindrical shell incorporating stator teeth, windings, and housing or cooling jacket effects. The model accommodates both continuous and piecewise variations in material properties and thickness. Based on First-Order Shear Deformation Shell Theory (FSDST), it accounts for shear deformation, rotary inertia, and trapezoidal stress distributions, enabling accurate prediction of axial, circumferential, torsional, and bending vibration modes. A segmentation approach is used along the axial direction, with artificial massless springs enforcing continuity and permitting general boundary conditions. Displacement fields are constructed using orthogonal Jacobi polynomials, and the eigenvalue problem is solved via the Rayleigh–Ritz method. Notably, the methodology allows accurate and efficient prediction of axisymmetric (breathing) modes in thick, non-uniform cylindrical shells – a capability rarely addressed in existing literature, despite its importance in Noise, Vibration, and Harshness (NVH) analysis. Validation against Finite Element Analysis (FEA) and Experimental Modal Analysis (EMA) on both generic cylindrical shells and a real Permanent Magnet Synchronous Machine (PMSM) stator shows excellent agreement, with natural frequency deviations typically below 5% and highly consistent mode shapes. The framework also achieves over 95% reduction in computational time compared to FEA, establishing it as a highly adaptable and practical tool for vibration analysis in electric motor design and NVH engineering applications.