Spring Damper System Research Articles

Analysis of the load‐bearing characteristics of hydraulic supports for top‐coal caving under the impact of coal and gangue

AbstractTo study the effect of different sizes and speeds of coal gangue falling on hydraulic supports for top‐coal caving discharge hydraulic support on the bearing characteristics of the hydraulic support, the ADAMS hydraulic support rigid‐flexible coupling analysis model was established. HyperMesh is used to flexibly process the hydraulic support, and the column and jack are equivalently replaced by spring damping system. By applying step loads of different sizes and speeds to simulate the impact force generated when the coal gangue falls on different positions of the cover beam, the dynamic response characteristics of the column, balance jack and other articulation points are obtained. Analyses show that: when the impact load is closer to the roof beam, the articulation point of the roof beam‐cover beam and the balancing jack are easy to be damaged. When the same impact load is applied to the cover beam, the faster the load is applied, the hydraulic support column and balancing jack may not be able to absorb and disperse the pressure effectively in time, resulting in the articulation points being subjected to a larger impact force, which is easy to cause damage or destruction. When different sizes and speeds of impact loads are applied to the cover beam, the latter has a greater impact on the dynamic response of the front and rear connecting rod articulation points and the cover beam‐roof beam articulation point than the former, and the hydraulic bracket will be more prone to vibration, deformation, and stress concentration, thus affecting the stability and safety of the bracket. The article is of guiding significance for designing and optimizing the structure and parameters of the hydraulic support, and improving the support performance and stability of the hydraulic support in the comprehensive release working face.

Trajectory-based breakup modelling for dense bubbly flows

A new model to predict the breakup of gaseous bubbles in a continuous liquid phase is developed. In the model each bubble is modelled as a spring–damper system, namely a Kelvin–Voigt element, while the outer force is derived by a Lagrangian analysis determining the largest stretching rate of the flow field below. The developed model is based on physical principles and no further arbitrary parameters have to be adjusted. Each bubble is observed on its way through the bubbly flow individually, taking into account its history along its respective path. With the implemented model numerical simulations in a wide range of scales are conducted, ranging from the laboratory scale of a vessel of 3L to the large industrial scale of 15m3. The simplicity of the model allows for a good cost to benefit ratio. In the present work, the achieved results are compared to experimental data obtained from optical measurements in a replica of a 200L aerated stirred tank reactor for various stirrer frequencies.

The effect of small internal and dashpot damping on a trapped mode of a semi-infinite string

The effect of small internal and dashpot damping on a trapped mode of a 1D-waveguide, that is, a semi-infinite string on a Winkler elastic foundation, has been investigated. At the edge of the string a mass–spring–damper system is attached. The string is assumed to have an internal damping. Four models for the internal damping are considered: air damping, Kelvin–Voigt damping, local Kelvin–Voigt damping, and damping related to time hysteresis. Depending on the internal damping and the parameters in the formulated problem, it will be shown that the amplitude of a trapped mode of the string can decrease or increase with time.

Discrete element method simulation of high-speed vehicle collisions with road barrier systems

AbstractThe behavior of road or perimeter protection barriers under vehicle impact are usually investigated based on crash tests and finite element (FE) numerical approaches, which are ether expensive or time-consuming. Several studies have proposed to reduce the computation time of the numerical analysis by substituting the complex FE models of vehicles using simplified mass–spring–damper system models. However, these models have drawbacks since consideration of different vehicle impact angles is difficult and they are unable to correctly simulate the risk of high-speed vehicle collision running over the barrier. In this paper, a new approach is proposed to simulate the collision of vehicles with barriers based on the discrete element method (DEM). Here, to save computation time only a handful of 3D non-spherical particles are used to represent the barrier and vehicle. These particles are generated based on the super-quadric function, which is capable of generating a variety of shapes needed for the model. The contact detection and evaluation are carried out based on discrete function representation of the particles with uniform sampling. The bond between two discrete elements is defined using a nonlinear cohesive beam model since the distance between the elements is relatively large. The simulation results obtained based on this approach are more accurate and complete than the simplified mass–spring models and computationally more efficient than the FE model.

Stability analysis of random fractional-order nonlinear systems and its application

The research on stability analysis and control design for random nonlinear systems have been greatly popularized in recent ten years, but almost no literature focuses on the fractional-order case. This paper explores the stability problem for a class of random Caputo fractional-order nonlinear systems. As a prerequisite, under the globally and the locally Lipschitz conditions, it is shown that such systems have a global unique solution with the aid of the generalized Gronwall inequality and a Picard iterative technique. By resorting to Laplace transformation and Lyapunov stability theory, some feasible conditions are established such that the considered fractional-order nonlinear systems are respectively Mittag-Leffler noise-to-state stable, Mittag-Leffler globally asymptotically stable. Then, a tracking control strategy is established for a class of random Caputo fractional-order strict-feedback systems. The feasibility analysis is addressed according to the established stability criteria. Finally, a power system and a mass–spring-damper system modeled by the random fractional-order method are employed to demonstrate the efficiency of the established analysis approach. More critically, the deficiency in the existing literatures is covered up by the current work and a set of new theories and methods in studying random Caputo fractional-order nonlinear systems is built up.

A parallel coupling framework for DEM-MBD: Model verification and application

Bulk material handling equipment can be numerically studied using the DEM-MBD method, where the particulate dynamics are solved by DEM (Discrete Element Method) and the motion characteristics of the mechanical components are modeled by MBD (Multi-Body Dynamics). In this work, a two-way coupling framework is proposed for the co-simulation of our self-developed DEM solver (DEMSLab) with the commercial MBD software (RecurDyn) using a parallel staggered coupling approach. To verify the proposed coupling method, the simulation result of a torsional spring damper system is compared with the corresponding analytical solution. After that, to assess the feasibility of this method in industrial-scale applications, a series of simulations involving a wheel loader is carried out. Different simulation conditions are adopted to reveal their impact on computational efficiency and simulation accuracy. These conditions include the mesh representation of the equipment geometry, the MBD time step size, and the coupling interval. An improved mesh simplification algorithm is proposed and used to reasonably simplify the surface mesh of the wheel loader, thus lowering the computational intensity of particle-wall interactions in DEM. The comparison results indicate that the computational time can be largely saved while the simulation accuracy remains considerably high. The MBD step size and coupling interval are crucial for numerical stability and should be selected carefully.

Multibody Dynamics and Terramechanics-based modeling and simulation of Quarter-Car with Suspension

Abstract While tires only compress when acted upon by a load in on-road scenarios, in off-road conditions, on the other hand, the tires not only undergo compression but also sinkage into the ground, in a manner that depends on the terrain. The tire-ground contact, in turn, affects the forces acting on the suspension system. Hence, it is necessary to study the vertical dynamic response of a system in off-road conditions by accounting for the terramechanics phenomenon (tire-terrain interface). The forces acting at the tire and terrain interface in off-road conditions have been studied in terramechanics separately; however, their integration with multibody systems is relatively less explored. In this paper, a multibody dynamic-based modeling and simulation of a quarter car with a linear spring-damper suspension system for off-road vehicles is presented. The generalized external forces are obtained using the Bekker-Wong based soil pressure-sinkage approach for two different kind of multibody systems interacting with sandy loam terrain. This model is integrated with the Tangent Space Ordinary Differential Equations of the quarter car and suspension system and solved using numerical integration techniques. Thus, by accounting for the terramechanics in the multibody system, the technique provides a more realistic response of the system in off-road scenarios.

Cluster consensus for nonlinear multi‐agent systems restricted with input saturation by event triggered control

AbstractThis article studies the cluster consensus problem for the nonlinear multi‐agent systems subject to input saturation under the context of event triggered control. Taking ordinary consensus object as a special case, this article considers the problem of cluster consensus. The event triggered mechanism is designed and the Zeno phenomenon is ruled out. The sufficient conditions of control protocol and range estimation of domain of attraction are formulated by the linear matrix inequalities for the constraints of input saturation and nonlinear terms existed in the system dynamics. Finally, the proposed results are validated by one example in the background of spring damping system.

Understanding wave energy converters dynamics: High-fidelity modeling and validation of a moored floating body

In ocean engineering, one of the most challenging phenomena to replicate is the interaction between waves and a moored floating body. Accurately evaluating such systems is essential for minimizing uncertainties, mitigating risks, and advancing technologies like wave energy converters. For this purpose, this study aims to develop a high-fidelity numerical model capable of reducing reliance on costly experimental campaigns during the device design phases. The model integrates a fluid dynamics module based on the Navier–Stokes equations, implemented in Star CCm+, with a mooring model utilizing a mass–spring–damper system, specifically MoorDyn. The primary objective is to introduce this coupled approach and demonstrate its efficacy through validation against experimental data from two distinct wave energy converters: ISWEC and PeWEC. The validation process encompasses comprehensive comparisons between simulated and observed kinematic behavior, mooring tensions, and crucially, pressure loads. Results indicate that the model is able to faithfully predict the complex phenomena involving a moored floating body, affirming the accuracy and reliability of the proposed coupling methodology. The coupling developed is available online link, where a simplified case study is present to show how to compile the library and add it in the numerical model.

Virtual Prototyping of the RM Active Grid®: a DEM-MBD Study

Numerical simulation is an established tool to improve knowledge of complex systems and to accelerate the development of new prototypes. In this contribution, the patented Active Grid® made by the company RM RUBBLE MASTER HMH GmbH is examined.In an initial step, representative system parameters (spring properties) are found via a multibody dynamic simulation; at this point, without particles acting on the system components. After that, the virtually defined Active Grid® system is loaded with particles in order to include the interaction effects of various bulk materials acting on the system’s mechanical components. For this purpose, a DEM-MBD co-simulation, extending the discrete element method (DEM) towards multibody dynamics (MBD) simulation, is performed, accounting for the bulk materials via DEM and the interacting system components via MBD. This bi-directional co-simulation enables the consideration of interactions between the bulk materials (the particles) and the driven spring-damper system (the moving system components).With this virtual prototype of the Active Grid®, performance benefits and characteristics in terms of screening efficiency for different material types and varying drive speeds are analysed. The overall aim is to achieve a scalable DEM-MBD model that allows virtual prototyping and, especially, optimisation for future system developments.

A nonlinear dynamic hysteresis model with magnetic–prestress–thermal coupling effect and dynamic electromagnetic losses of a giant magnetostrictive actuator

Compared with traditional actuators, the giant magnetostrictive actuator has the merits of fast response, high accuracy, and high reliability and has been widely applied. However, its performance is affected by the electromagnetic loss and the temperature, prestress, and magnetic coupling effect. In order to accurately analyze its performance, it is necessary to establish a nonlinear dynamic model including the electromagnetic loss and the magnetic–prestress–thermal coupling effect. First, based on the field separation approach, the magnetic fields generated by the eddy current loss and the anomalous loss are obtained and added to the Jiles–Atherton model. Second, the magnetostrictive model is given with the magnetic–prestress–thermal coupling effect. Finally, assuming the transmission of the giant magnetostrictive actuator as a mass–spring–damper system, a nonlinear dynamic hysteresis model with magnetic–prestress–thermal coupling effect and dynamic electromagnetic losses of a giant magnetostrictive actuator is developed. Based on this model, the output displacement curves of the giant magnetostrictive actuators under different driving currents and frequencies are given. The comparison with the experimental results shows that this model agrees well with the experiment.

Group consensus of nonlinear semi-Markov multi-agent systems by a quantity limited controller

This paper solves the group consensus problem of incremental quadratic constraints nonlinear multi-agent systems with semi-Markov switching parameters via a quantity limited controller. The quantity limited controller is designed according to the stationary probability distribution of the system modes, and the number of controllers can be selected from 1 to the number of system modes. Therefore, the controller can be applied in cases where there is a mismatch between the number of system modes and the number of controllers. Next, the more general incremental quadratic constraint is used to handle the nonlinear terms. Finally, in the simulation section, the method of adding topology links is used to implement external equitable partitions of arbitrary topologies, and the validity of the proposed method is verified by a spring damping system.

A Simplified Model to Predict the Repeated Shear Strain during the Cyclic Triaxial Test by Using an Elastic Coefficient-Damping Ratio System

Some researchers in past years have tried to develop a simplified method for analyzing soil liquefaction. However, the correctness of the pore water pressure in the model will affect the results. In addition, the formulas derived are not easy, and the exact parameters of the model are difficult to obtain. This study used a mass-spring-damping system to simulate the repeated strain of liquefaction cyclic triaxial tests. Because the model is simple and the parameters are easy to understand and obtain, it also shows the extensibility of this model. During the parameter study, damping coefficient c and spring coefficient k parameters decreased with the increasing cyclic number. Preliminary results of the research show that this model can further simulate the repeated strain obtained by cyclic triaxial tests without considering the variation of effective stress during cyclic loading. Four samples were used to verify the model’s correctness, and their boring sites were found in Yunlin areas, Taiwan. Simulation results show that the spring-damping system is feasible for simulated cyclic triaxial tests because the simulated results correlate to the testing results in trend. Generally, the first cycle number simulation will be less accurate because the pore water pressure of the specimen changes rapidly when the performance has just started. In contrast, the increase in subsequent cycles may be biased due to cyclic stress variation and soil plasticity during simulation. In the future, pure sand specimens created in the laboratory will be suggested for simulation.

Analytical solution for simplifying the pile-soil interaction to a spring-damping system under horizontal vibration

An analytical solution is developed to investigate the model of simplifying the pile-soil interaction to a spring-damping system when the horizontal earthquake input or the top of the model is subjected to horizontal dynamic load. Based on Euler-Bernoulli theory, the dynamic equilibrium equations of pile in soil and air are established, respectively. Then, utilizing the corresponding boundary conditions, potential function decomposition, and transfer matrix method, the analytical expression of impedance at the pile head whether the horizontal earthquake input or the top of the system is subjected to horizontal dynamic load can be presented. Furthermore, the model of the pile-soil complex interaction can be simplified as a spring-damping system according to the stress equilibrium at the pile bottom in the air. Moreover, the rationality of the present solution (without simplification) is verified by comparison with existing methods, and then the difference between the present solution (without simplification) and the spring-damping system (simplification) is also compared. Finally, the influence of the parameter variation in the pile buried in the soil and soil free-field on the simplified model are discussed. The research results will be instructive for the simplification of numerical model for pile-soil interaction.

Research on the hydraulic support face guard mechanism and coupling characteristic of rib spalling in large mining heights

In view of the problem of poor coupling adaptability and easy rib spalling of coal wall in large mining height comprehensive mining, based on the effective inhibition effect of face guard mechanism on coal wall spalling, the structural characteristics and bearing capacity of different structural forms of the face guard mechanism are compared and analyzed. According to the surrounding rock adaptability of the face guard mechanism, established a numerical analysis model for rigid-flexible coupling of the face guard mechanism under different spalling forms. In order to accurately simulate the stress state of the protective mechanism, a variable stiffness spring damping system is used to replace the hydraulic cylinder. The load-bearing performance and response characteristics of the face guard mechanism under rib spalling coupling conditions were analyzed by applying uniform normal load and impact load to the face guard. The findings indicated that, the integral-type face guard mechanism has a better effect on suppressing rib spalling. When the face guard mechanism bears the static load of the coal wall, the entire response process of the face guard jack can be divided into three stages: initial support, increasing resistance bearing, constant resistance bearing; both the impact load position and the coupling state of the rib spalling will affect the characteristics of force transmission at the face guard mechanism’s hinge point, the hinge point between the extensible canopy and the primary face guard is most sensitive to biased load. The research results can provide reference for optimizing the face guard mechanism of large mining height hydraulic support and improving the reliability of coal wall support.

Virtually constrained generalized relative motion modeling and a control parameter optimizer for automatic carrier landing

PurposeThis paper aims to propose a novel control scheme and offer a control parameter optimizer to achieve better automatic carrier landing. Carrier landing is a challenging work because of the severe sea conditions, high demand for accuracy and non-linearity and maneuvering coupling of the aircraft. Consequently, the automatic carrier landing system raises the need for a control scheme that combines high robustness, rapidity and accuracy. In addition, to exploit the capability of the proposed control scheme and alleviate the difficulty of manual parameter tuning, a control parameter optimizer is constructed.Design/methodology/approachA novel reference model is constructed by considering the desired state and the actual state as constrained generalized relative motion, which works as a virtual terminal spring-damper system. An improved particle swarm optimization algorithm with dynamic boundary adjustment and Pareto set analysis is introduced to optimize the control parameters.FindingsThe control parameter optimizer makes it efficient and effective to obtain well-tuned control parameters. Furthermore, the proposed control scheme with the optimized parameters can achieve safe carrier landings under various severe sea conditions.Originality/valueThe proposed control scheme shows stronger robustness, accuracy and rapidity than sliding-mode control and Proportion-integration-differentiation (PID). Also, the small number and efficiency of control parameters make this paper realize the first simultaneous optimization of all control parameters in the field of flight control.

High force compression mode to Shear mode piezoelectric energy harvesting

This study is to develop structures with the ability to convert a compression force into radial extension or shear force, to increase power output through piezo shear mode. In this work, a piezoceramic-spring system was developed with two types of force-spreading spring configurations, the Belleville disc springs and the crinkle washer. A force loading profile is applied to a piezoceramic element and structure causing the force to be distributed in different directions when compared to a conventional helical spring damping system or compression. The performances of these novel structures were studied using Multiphysics simulation and experiments. This work shows that both the Belleville disc and crinkle washer produce improved energy output between 15 and 22% compared to compression alone, whilst the Belleville disc spring outperformed a crinkle washer in both simulations and experiments. The results show that converting compression to shear force in energy harvesting could be a potential approach to increase the energy efficiency and energy density.

Controlling chaotic vocal fold oscillations in the numerical production of vowel sounds

Lumped mass models have been studied in depth to unveil the complex nonlinear physics of phonation. Even in the case of simple symmetric models, slight changes in muscle restoring forces or excessive subglottal pressure can cause abnormal or even chaotic vocal fold oscillations. In a recent work, it was shown that it was possible to device a theoretical pacemaker for phonation that could render the chaotic motion regular again. This consisted of attaching an additional mass–spring–damper system to the vocal fold model, the damping of which could be adjusted according to an altering energy chaos control strategy. The chaos of phonation is low-dimensional and one may wonder whether it has a profound effect in voice production and, if so, whether the proposed phonation pacemaker could compensate for it. For this purpose, we compute the time evolution of the glottal volume velocity generated by normal, chaotic and controlled oscillations of the vocal folds and convolve it with the impulse response of magnetic resonance imaging (MRI) geometries of the human vocal tract, corresponding to the vowels /ɑ/, /i/ and /u/. The impulse response for each vowel is obtained from the solution of the wave equation by the finite element method, when a Gaussian pulse is prescribed as a boundary condition in the glottis of the vocal tract. It will be demonstrated that the chaotic vibration of the vocal folds severely distorts the vowel sounds and that the proposed control strategy is able to recover with high quality the vowels produced in normal phonation. Audiovisual files are provided to support the objective results of the phenomena in terms of spectral and time analysis of the train of glottal pulses generated by the vocal folds and the produced vowel sounds.

Graph oscillators: Physics-guided graph modeling of mass–spring–damper systems for trajectory prediction and damage localization

Recognizing that a multiple-degree-of-freedom mass–spring–damper system can be viewed as a group of connected nodes, this paper presents a novel computational framework that learns such coupled oscillations by a graph, a mathematical structure describing pairwise connections between objects. Further reinforced by an incomplete equation of motion, distributed neural networks and an anti-symmetric coupling constraint, we can learn unknown coupling mechanisms (or nodal interactions in the language of graph models) using limited data. The proposed physics-data-hybrid method demonstrates a promising predictive capability even for unseen control inputs, outperforming three black-box and grey-box counterparts in synthetic and experimental studies. In addition to its predictive capability, the distributed parameterization of nodal interactions allows us to identify local anomalies by evaluating updates after short transfer learning. While limits of the current method exist, it displays the potential of a generalizable and interpretable meta-model for predicting nonlinear trajectories and identifying the system’s status.

A Dual Triggering Scheme to Adaptive Fuzzy Resilient Control of Switched Nonlinear Systems Against Mixed Attacks.

A dual event-triggered adaptive fuzzy resilient control scheme for a class of switched nonlinear systems with vanishing control gains under mixed attacks is proposed in this article. The scheme proposed achieves dual triggering in the channels of sensor-to-controller and controller-to-actuator by designing two new switching dynamic event-triggering mechanisms (ETMs). An adjustable positive lower bound of interevent times for each ETM is found to preclude Zeno behavior. Meanwhile, mixed attacks, that is, deception attacks on sampled state and controller data and dual random denial-of-service attacks on sampled switching signal data, are handled by constructing event-triggered adaptive fuzzy resilient controllers of subsystems. Compared with the existing works for switched systems with only single triggering, more complex asynchronous switching caused by dual triggering and mixed attacks and subsystem switching is addressed. Further, the obstacle caused by vanishing control gains at some points is eliminated by proposing an event-triggered state-dependent switching law and introducing vanishing control gains into a switching dynamic ETM. Finally, a mass-spring-damper system and a switched RLC circuit system are applied to verify the obtained result.