Meccanica最新文献

This work proposes an efficient numerical methodology to simulate the non-smooth vibro-impact dynamics between two one-dimensional continuums, more specifically, two taut strings. At the outset, we invoke Galerkin’s projection to render the partial differential equation (PDE) governing the dynamics of the infinite-dimensional continuum to a finite-dimensional system of ordinary differential equations (ODEs). Initially, we address the complex impact interactions between the systems through a transformation from modal-to-physical coordinates on a spatially discretized grid. Subsequently, the impact forces and the post-impact velocities are obtained using the impulse-momentum principle and the coefficient of restitution. Notably, the methodology eliminates the necessity of detecting the time instant of the impact event, thereby rendering the procedure computationally efficient. The temporal evolution is handled using a modified Moreau’s midpoint scheme, where the impact force at a given time step is found explicitly. The considered strings, being non-dispersive, admit closed-form solutions for specific cases like point obstacles and smooth sinusoidal and flat obstacles. The solutions were obtained by Cabannes et al. (H. Cabannes, “Presentation of software for movies of vibrating strings with obstacles”, Applied Mathematics Letters 10 (5) (1997) 79-84.) in terms of travelling waves, invoking the method of characteristics. We compare the results from the presented methodology with these closed-form solutions and show that they match extremely well. Furthermore, to show that the proposed methodology is computationally more efficient than other methods, we compare the results with the Galerkin−Ivanov numerical method. We once again observe extremely good correspondence between the results and exhibit significant computational advantages of the proposed approach for several test cases considered herein. The numerical investigations provide evidence to support the method’s efficacy in predicting precise and energy-conserving responses for different parameter ranges.

There are some simplified parameters in the traditional dynamic model of the planetary gearbox (PGB), which leads to the consistency of simulated vibration signals with the measured vibration signals being inferior. In addition, the accuracy of the simulated signals is inferior, which reduces the accuracy of the PGB fault diagnosis based on the simulated signals. To address the above problems, a method for optimization of the PGB dynamics model based on the Improved Grasshopper Optimization Algorithm (I-GOA) and global sensitivity analysis is proposed. Firstly, an I-GOA based on adaptive social force factor and pattern search is proposed to address the problems of slow convergence speed, low search accuracy, and imbalance between global and local search ability during parameter optimization by Grasshopper Optimization Algorithm (GOA). Secondly, a sensitive feature selection method is proposed based on univariate evaluation and Pearson correlation coefficient. The method reduces the number of features for fault diagnosis, lowers the problem dimension, and is applied to the measured signals to select sensitive features for PGB faults. The method establishes a sensitive feature set to planetary gear tooth wear faults. Thirdly, to select the critical optimization parameters of the dynamical model, a model parameter selection method of Kriging surrogate model combined with Sobol’ global sensitivity analysis is proposed. Finally, the sensitivity features of the measured and simulated vibration signals are calculated by characteristic expressions, and the Euclidean distance loss of the two signals is used as the objective function of model optimization. The parameters of the PGB dynamic model are updated using I-GOA, and the dynamic model of planetary gear wear failure in PGB experimentally verifies the proposed method. Finally, the simulation experiment verifies that the proposed method is feasible and effective.

This paper presents a theoretical procedure for obtaining the dissipation function for anisotropic rigid-plastic materials, the yielding of which is governed by the Barlat and co-workers-like plasticity criteria (Int J Plast 21:1009–1039, 2005. https://doi.org/10.1016/j.ijplas.2004.06.004) incorporating several linear transformations of the stress in generic isotropic plasticity models, extending the proposal of Karafillis and Boyce (J Mech Phys Solids 41:1859–1886, 1993. https://doi.org/10.1016/0022-5096(93)90073-o). The underlying isotropic yield criterion can be very general including possible Lode angle effects in the material behaviour. The seeked dissipation function is needed for the construction of the macroscopic behavior of voided materials when it is for instance combined to appropriate representative volume elements of these materials and associated kinematically admissible velocity fields satisfying uniform boundary conditions at their boundary in the spirit of the Gurson’s approach (J Eng Mater Technol 99:2–15, 1977. https://doi.org/10.1115/1.3443401) to ductile fracture.

In differential gear systems, low reduction ratio (LRR) face gear drives are frequently overlooked because of the severe edge contact problems and the loss of meshing features in the toe region. This study presents a combination of pinion tooth crowning modification and the development of a mixed elastohydrodynamic lubrication (EHL) wear model in order to enhance and evaluate the contact performance of LRR face gear drives. The bearing contact is localized by the longitudinal crowning of the pinion tooth surface, where the pinion and shaper have the same number of teeth. Simultaneously, by analyzing gear meshing characteristics and integrating the sliding wear law with EHL theory while taking rough surfaces into consideration, the EHL wear model is established. Lubrication and wear analyses at two critical meshing points under the ISO 6336 standard show that modification parameters and the pinion's axial mounting position affect lubrication and sliding wear. Specifically, increasing the modification radius or reducing the axial mounting distance of the pinion can improve lubrication performance, thus providing an effective solution for the contact issues of LRR face gear pairs.

The tooth load in heavy-duty wind turbine gearboxes is significantly affected by the structural deformations of the planetary gear train (PGT) with the interference fit. In this study, a dynamic modeling method for gear meshes is proposed considering the comprehensive structure flexibility and dynamic tooth contact. The condensation theory of finite elements is utilized to establish the ring gear and carrier, developing correlations between the point of action and elastic support. Furthermore, the dynamic mesh deformation considering the influences of pin-axis deviation caused by the interference fit is deduced. Finally, a dynamic model of PGT with flexible pins is established and subsequently verified. The pin-axis deviation resulting from the interference fit and its impact on tooth loads and system vibrations is investigated. The results indicate that the main cause of unbalanced tooth loads is the asymmetric deformation of the carrier pin. Additionally, in the resonance region, this phenomenon will worsen, and there is a significant difference between the dynamic meshing stiffness and the quasi-static meshing stiffness. As the interference-fit magnitude increases, the pin-axis deviation amplifies, leading to a more severe tooth load imbalance.

The limited micro-amplitude of piezoelectric discs is a critical factor constraining the output performance of valveless piezoelectric pumps. To address this limitation and enhance the volumetric change within the pump chamber, this study proposes a resonant valveless piezoelectric pump equipped with a Tesla valve. By decoupling the pump chamber diaphragm from the excitation unit and leveraging the principle of resonance, the diaphragm’s amplitude is amplified, thereby improving the overall output performance of the piezoelectric pump. Additionally, the "diode effect" of the Tesla valve is employed to achieve unidirectional fluid flow. First, the motion differential equation for the excitation unit is derived based on the operating principles of the resonant pump, and a force analysis of the pump chamber diaphragm is conducted. Second, the finite element method is used to simulate the flow velocities in both forward and reverse directions through the Tesla valve. Finally, a prototype of the pump is fabricated and experimentally tested. The experimental results indicate that the resonant pump achieves a maximum output flow rate of 108 mL/min when the mass block is 15 g, the driving frequency is 35 Hz, and the driving voltage is 150 V. Interestingly, increasing the stiffness of the spring leads to a decrease in the output flow rate. For instance, when the spring diameter is 14 mm, the flow rate reduces to 83 mL/min. Furthermore, increasing the shunt angle of the Tesla valve improves the pump's output performance; however, when the angle exceeds 60°, the flow rate decreases to 77.7 mL/min.

The aim of the paper is to clarify the semantic and thus the difference between tyre rolling resistance and tyre rolling loss. Reference is exclusively made to longitudinal forces. The focus is on which are the actual forces and moments that cause a dissipated power during tyre rolling. The equilibrium equation for rotation of the wheel is unable to describe which are such actual forces and moments. In accordance with the existing literature, the power balance of rolling tyre is more suitable to identify the actual forces and moments causing dissipated power. We propose to refer to “rolling resistance” when the longitudinal slip is vanishing or low and to refer to “rolling loss” when the longitudinal slip is relatively high. A new index defining the rolling loss is proposed, namely the tyre rolling dissipation index (TRDI). The theoretical investigation is substantiated by an experimental activity performed via a new trailer for tyre testing. The rolling resistance torque, the external applied torque, the wheel axle height, the longitudinal force at the hub and the kinematics of the rim have been measured and combined to describe the TRDI. Results shows that tyre rolling loss increases as a braking torque is applied to the wheel and the effect of the TRDI is shown as function of longitudinal slip. A practical rule is proposed, stating that the ratio of tyre dissipated power to the total dissipated power is nearly equal to the longitudinal slip.

The reduced multibody system transfer matrix method is a multibody system dynamics method adopting tree topology description and utilizing joint coordinates as the generalized coordinates of the system. For a multibody system containing closed loops, it is necessary to “cut” a joint in each inner loop, which will be replaced by geometric constraint equations confined on the generalized coordinates of the spanning tree system, as well as a pair of internal forces in equilibrium implied on the two connected body elements. The reduced multibody system transfer matrix method employs relatively lower order coefficient matrices that are independent of the degrees of freedom of the system, resulting in faster computational speed compared to those methods that establish and solve the global dynamics equations of the system characterized by the global inertial matrix, whose dimension is no less than the degrees of freedom of the system, no matter utilizing joint coordinates or not. However, in the process of multibody system dynamics modeling, the redundancy in constraints, which causes rank deficiency of the constraint equations’ Jacobian matrix, is an unavoidable problem. In this paper, an algorithm based on the singular value decomposition is proposed to resolve the singularity problem in the context of reduced multibody system transfer matrix method when handling redundant constraints. The singular value decomposition is utilized to compute the Moore-Penrose generalized inverse, resulting in the minimum norm solution for the constraint forces at the cut-off joints within closed-loop constraints. The proposed method is validated by two numerical examples.

Sealing technology is critical for the reliability and efficiency of mechanical systems, especially in rotating shaft applications. Traditional ferrofluid (FF) seals, while effective in narrow gaps (0.1–0.3 mm), face significant limitations in maintaining effective sealing under large gap conditions (more than 0.3 mm). To address this challenge, a magnetorheological fluid (MRF) seal optimized for high-speed dynamic applications was proposed. Firstly, a sealing structure was designed, and the rheological properties of MRF were characterized. Then, theoretical models for both FF and MRF seals were derived to analyze their operating principles and performance differences. A custom test bench was constructed to evaluate static sealing performance at 0.1 mm and 0.4 mm gaps and dynamic sealing performance at shear velocities of 0.2, 0.4, 0.6, 0.8, and 1.0 m/s. Experimental results demonstrated that MRF seals achieve higher pressure differentials compared to FF seals, particularly in large gap scenarios. These findings suggest that MRF seals offer a promising alternative for advanced sealing applications in mechanical systems.

Tuned Mass Dampers (TMDs) and Tuned Liquid Column Dampers (TLCDs) are widely recognized passive vibration control devices used to reduce structural vibrations. While TMDs have been extensively studied for mitigating the seismic responses of multi-story buildings considering Soil-Structure Interaction (SSI), the efficiency of TLCDs in these conditions remains largely unexplored. Furthermore, a direct comparison of these devices under similar conditions has not been conducted. Then, to address these gaps, this study investigates the efficiency of TLCDs and compares them to TMDs in reducing seismic-induced vibrations, focusing on the influence of SSI. The control performance of both devices depends on various parameters, primarily the frequency and damping ratios. Therefore, the Mouth Brooding Fish (MBF) metaheuristic algorithm is applied to optimize these parameters, accounting for SSI effects. To evaluate the different efficiency between TMDs and TLCDs under SSI conditions, three types of shear buildings are considered: an eight-story, a sixteen-story and a forty-story structure. The seismic responses of the uncontrolled, TMD-controlled, and TLCD-controlled buildings are examined under twenty-two far-field and fourteen near-field earthquakes, considering both fixed-base and flexible-base scenarios. Results indicate that while both devices significantly reduce seismic responses, TMDs generally outperform TLCDs, particularly in taller buildings where the impact of SSI is more significant. Further, this study highlights that neglecting SSI in the design of these devices may lead to an overestimation of their effectiveness, especially in softer soils, emphasizing the importance of considering SSI in the optimization process for accurate and reliable outcomes.