Dynamic behavior of an agricultural power take-off driveline for rattle noise reduction: Part 1. Effect of spline tolerance on the power take-off rattle noise

An agricultural tractor has a power take-off (PTO) driveline that is directly connected to the engine to improve its power transmission efficiency. The PTO driveline comprises various mechanical components coupled by a spline joint. The spline coupling tolerance causes collisions between various mechanical parts of the PTO driveline and affects gear collision, thereby causing rattle noise. Therefore, the aim of this study is to conduct a dynamic behavior analysis to predict the gear rattle noise level of a PTO driveline. The dynamic behavior of the PTO driveline was analyzed through 1D simulations, and the results confirmed that the dynamic behavior changes according to rotation speed. Experimental verification of the dynamic behavior analysis results confirmed that the dynamic behavior changes as the main engine excitation-component amplification changes and then decreases at a relatively high rotation speed. Additionally, the dynamic behavior changes of the PTO driveline resulted in a jumping phenomenon that occurs rapidly at a specific rotation speed. The amplification of the engine’s main components was reduced from 3 to 4 times to 1.2 times owing to the jumping phenomenon; the noise level of the gear rattle was also reduced by approximately 10.9 dB(A).     

Dynamic model and performance analysis of landing buffer for bionic locust mechanism

The landing buffer is an important problem in the research on bionic locust jumping robots, and the differ-ent modes of landing and buffering can affect the dynamic performance of the buffering process significantly. Based on an experimental observation, the different modes of landing and buffering are determined, which include the different numbers of landing legs and different motion modes of legs in the buffering process. Then a bionic locust mechanism is established, and the springs are used to replace the leg muscles to achieve a buffering effect. To reveal the dynamic performance in the buffering process of the bionic locust mechanism, a dynamic model is established with different modes of landing and buffering. In particular, to analyze the buffering process conveniently, an equivalent vibration dynamic model of the bionic locust mechanism is proposed. Given the support forces of the ground to the leg links, which can be obtained from the dynamic model, the spring forces of the legs and the impact resistance of each leg are the important parameters affecting buffering performance, and evaluation principles for buffering performance are proposed according to the aforementioned parameters. Based on the dynamic model and these evaluation principles, the buffer-ing performances are analyzed and compared in different modes of landing and buffering on a horizontal plane and an inclined plane. The results show that the mechanism with the ends of the legs sliding can obtain a better dynamic per-formance. This study offers primary theories for buffering dynamics and an evaluation of landing buffer performance, and it establishes a theoretical basis for studies and engineer-ing applications.     

A coupled zigzag theory for the dynamics of piezoelectric hybrid cross-ply plates

A recently developed coupled third-order zigzag theory for the statics of piezoelectric hybrid cross-ply plates is extended to dynamics. The theory combines a third-order zigzag approximation for the in-plane displacements and a sub-layerwise linear approximation for the electric potential, considering all components of the electric field. The nonuniform variation of the transverse displacement due to the piezoelectric field is accounted for. The conditions for the absence of shear traction at the top and bottom surfaces and continuity of transverse shear stresses in the presence of electromechanical loading are satisfied exactly, thereby reducing the number of displacement variables to five, which is the same as in a first- or third-order equivalent single-layer theory. The governing equations of motion are derived from the extended Hamilton's principle. The theory is assessed by comparing the Navier solutions for the free and forced harmonic vibration response of simply supported plates with the exact three-dimensional piezoelasticity solutions. Comparisons for hybrid test, composite and sandwich plates establish that the present theory is quite accurate for the dynamic response of moderately thick plates.     

The frequency response of dynamic friction: Model comparisons

Any linearised theory of the initiation of friction-excited vibration via instability of the state of steady sliding requires information about the dynamic friction force in the form of a frequency response function for sliding friction. Recent measurements of this function for an interface consisting of a nylon pin against a glass disc are used to probe the underlying constitutive law. Results are compared to linearised predictions from the simplest rate-state model of friction, and a rate-temperature model. In both cases the observed variation with frequency is not compatible with the model predictions, although there are some significant points of similarity. The most striking result relates to variation of the normal load: any theory embodying the Coulomb relation F∝N would predict behaviour entirely at variance with the measurements, even though the steady friction force obtained during the same measurements does follow the Coulomb law.     

Slip, stick, and reverse slip characteristics during dynamic fibre pullout

Inertial effects in the mechanism of fibre pullout (or push-in) are examined, with emphasis on how the rate of propagation of stress waves along the fibre, and thence the pullout dynamics, are governed by friction and the propagation of companion waves excited in the matrix. With a simple shear lag model (assuming zero debond energy at the fibre/matrix interface), the effect of uniform frictional coupling between the fibre and the matrix is accounted for in a straightforward way. Analytical solutions are derived when the pullout load increases linearly in time. The process zone of activated material is generally divided into two or three domains along the axis of the fibre. Within these domains, slip in the sense implied by the load, slip in the opposite sense (reverse slip), and stick may be observed. The attainable combinations define three regimes of behavior, which are realized for different material parameter values. The elastodynamic problem is also solved more accurately using a plane stress finite element method, with friction represented by an interfacial cohesive zone. The predictions of the shear lag theory are broadly confirmed.     

Modeling the dynamic behavior of shape memory alloys

The paper studies the single degree of freedom vibration of a rigid mass suspended by a thin-walled shape memory alloy tube under torsional loading. The behavior is analyzed for the cases of quasiplasticity (low temperatures) and pseudoelasticity (high temperatures) on the basis of an improved version of the Müller–Achenbach model. To illustrate the strong hysteresis-induced damping capacity and the non-linear vibration characteristics, both, free and forced vibrations are considered in the first part of the paper. This is done on the basis of an isothermal version of the model, while the second part of the paper focuses on the effect of non-constant temperature caused by the rate-dependent release and absorption of latent heats.     

Electric field-induced surface transformations and experimental dynamic characteristics of dielectric elastomer membranes

Acute and tunable surface transformations of a monolithic structure by application of an electric field have immediate significance for adaptive structures, morphing concepts and optical applications. Dielectric elastomer (DE) membranes are electric field-responsive materials typically employed as large strain electrostatic actuators. In this paper, it is demonstrated that an electric field will generate several symmetric surface shapes analogous to the mode shapes in the classical drumhead or stretched membrane problem. In a previous experimental study, a single surface transformation creating ripples or waves on an initially smooth surface was observed for an electrically excited DE membrane. The unexpected result led to the development of an experimental setup that would facilitate extensive characterization of the dynamic surface transformations of dielectric elastomer membranes. The new results clearly show that the electric field can be used to tune the patterns of the DE surface. Furthermore, the membrane will go through resonance when a periodic electric field is applied if the system conditions are favorable, which has not been observed before now. This presents a unique opportunity to increase the output displacement of DE membranes without electrically overloading the membrane. The experiments show that increasing the size of the chamber onto which the membrane is clamped will increase the peak deformation as well as cause the membrane's resonance peaks to shift and change in number. For DE membranes driven at 1.5 kV, at the smallest chamber volume, the maximum actuation displacement is 81 μm; while at the largest chamber volume, the maximum actuation displacement is 1431 μm. This corresponds to a 1767% increase in maximum pole displacement. The dependence on chamber volume suggests that under dynamic conditions a systems level analysis is needed for DE actuators. The effect of voltage offset as a means of modulating the dynamic deformation response is also reported in this study.     

On the long-term response of elastic-perfectly plastic solids to dynamic cyclic loads

It is shown that the long-term response of an elastic-perfectly plastic solid subjected to dynamic actions cyclically varying in time is characterized by stresses, plastic strain rates and velocities that are all periodic with the same period of the external actions, and are in perfect analogy with the quasi-static case; on the other hand, plastic strains and displacements are in general nonperiodic (except in case of alternating plasticity) and may increase indefinitely (except when elastic or plastic shakedown occurs). Besides, the work performed by the external actions in the steady cycle equals the work performed by the elastic stresses (i.e. pertaining to the elastic response of the body to the same actions) through the plastic strain rates.

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Sommario Per un solido elastico perfettamente plastico soggetto ad azioni cicliche dinamiche si mostra che la risposta a lungo termine è caratterizzata da tensioni, deformazioni plastiche incrementali e velocità tutte periodiche con lo stesso periodo delle azioni esterne, in analogia di quanto avviene nel caso quasi-statico; per contro le deformazioni plastiche e gli spostamenti sono in generale non periodici (tranne nel caso di plasticità alternata) e possono crescere indefinitamente (tranne nel caso di adattamento elastico o plastico). Inoltre il lavoro compiuto dalle azioni esterne in un ciclo stazionario risulta eguale al lavoro delle tensioni elastiche (cioè ottenute come risposta puramente elastica del solido alle stesse azioni) attraverso le deformazioni plastiche incrementali.

     

A hybrid force model to estimate the dynamics of curved legs in granular material

Robot locomotion on rigid terrain or in fluids has been studied to a large extent. The locomotion dynamics on or within soft substrates such as granular material (GM) has not been fully investigated. This paper proposes a hybrid force model to simulate and evaluate the locomotion performance of a legged terrestrial robot in GM. The model incorporates an improved Resistive Force Theory (RFT) model and a failure-based model. The improved RFT model integrates the force components of individual leg elements over the curved leg portion submerged in GM at any moment during a full period of leg rotation. The failure-based model is applied in a bar drag model to yield the normal and the lateral forces of the individual RFT elements as functions of the locomotion depth and speed. The hybrid model is verified by the coincidence between the theoretical predictions and the experimental results. The hybrid model is used to analyze the effects of angular velocity and leg shape with high precision and can guide the design of the legs with any profiles. Our study reveals that the interactions between locomotor and substrate are determined by the locomotor structural characteristics, the nature of the substrate, and the control strategy.     

双波护栏-汽车碰撞动力响应与吸能机理研究

我国西部山岭重丘区山高谷深,高速公路跨线天桥、弯道及坡道较多,这些特殊路段的防撞设施多采用立柱加密的双波护栏.通过ANSYS/LS-DYNA有限元数值仿真,对加密立柱双波护栏在汽车碰撞作用下的动力响应进行了研究,分析了双波护栏的碰撞能量转换与吸能机理,结果表明加密立柱的双波护栏对车辆碰撞具有良好的吸能、导向作用.     

On the dynamic electromechanical loading of dielectric elastomer membranes

Dielectric elastomer actuators (DEAs) have received considerable attention recently due to large voltage-induced strains, which can be over 100%. Previously, a large deformation quasi-static model that describes the out-of-plane deformations of clamped diaphragms was derived. The numerical model results compare well with quasi-static experimental results for the same configuration. With relevance to dynamic applications, the time-varying response of initially planar dielectric elastomer membranes configured for out-of-plane deformations has not been reported until now. In this paper, an experimental investigation and analysis of the dynamic response of a dielectric elastomer membrane is reported. The experiments were conducted with prestretched DEAs fabricated from 0.5 mm thick polyacrylate films and carbon grease electrodes. The experiments covered the electromechanical spectrum by investigating membrane response due to (i) a time-varying voltage input and (ii) a time-varying pressure input, resulting in a combined electromechanical loading state in both cases. For the time-varying voltage experiments, the membrane had a prestretch of three and was passively inflated to various predetermined states, and then actuated. The pole strains incurred during the inflation were as high as 25.6%, corresponding to slightly less than a hemispherical state. On actuation, the membrane would inflate further, causing a maximum additional strain of 9.5%. For the time-varying pressure experiments, the prestretched membrane was inflated and deflated mechanically while a constant voltage was applied. The membrane was cycled between various predetermined inflation states, the largest of which was nearly hemispherical, which with an applied constant voltage of 3 kV corresponded to a maximum polar strain of 28%. The results from these experiments reveal that the response of the membrane is a departure from the classical dynamic response of continuum membrane structures. The dynamic response of the membrane is that of a damped system with specific deformation shapes reminiscent of the classical membrane mode shapes but without same-phase oscillation, that is to say all parts of the system do not pass through the equilibrium configuration at the same time. Of particular interest is the ability to excite these deformations through a varying electrical load at constant mechanical pressure.     

Systematic closed form modeling of hybrid parameter multiple body systems

Presented in this paper is a systematic approach to modeling non-holonomic hybrid parameter multiple body systems. The continuum bodies are represented with the postulates usually associated to the non-linear theories, the Timoshenko (like) beam theories, the higher order plate and shell theories, and the rational theories (e.g. rods) with intrinsic rotary inertia properties.The methodology is an extension of previous work. It is founded in variational principles, but uses vector algebra to eliminate tedium. The variational nature of the methodology allows rigorous equation formulation providing not only the complete non-linear hybrid differential equations, but also the boundary conditions. The methodology is formulated satisfying general non-holonomic constraints; it produces a minimal realization. The spatial dimensions of the continuua are not restricted and the inter-body connections are completely general.To demonstrate the application of the technique, a two-link elastic pendulum or manipulator is modeled. The algorithmic modeling steps are demonstrated. Numerical simulations are presented.     

On the efficacy of pseudo-coordinates—Part 2: moving boundary constraints

In this paper an argument is presented in favor of utilizing felicitous or natural coordinates in the model formulation of complex hybrid parameter multiple body mechanical systems (HPMBS). Specifically for this paper, HPMBS that consist of continuua that are subjected to spatially and temporally varying non-holonomic boundary conditions. This is the second paper of a two part series of papers that is presented to clarify the novelty and usefulness of a recently developed Gibbs-Appell type projection based HPMBS modeling tool. The purpose of the paper is to show that with the novel use of pseudo-coordinates and speeds (as defined by the author) it is completely natural to provide minimal configuration space dimensionality yet still retain rigorous analytical formulation tractability.Presented in this work, as a demonstrative arguing point, is the development of the hybrid parameter motion equations for a rolling flexible-disk material cutting device. This device consists of a circular flexible continuum (the cutter) along with the requisite mounting rigid hub and handle. This non-holonomically constrained device is modeled executing spatial motion constrained to the plane via moving constraints applied to the boundary of the planar continuum. Also included in this work are numerical results bolstering the claims made herein. These numerical results demonstrate that the methodology elucidated provides low-order models suitable for modeling complicated devices. These low-order models are in contrast to the current modeling trend of ever-increasing degrees of freedom.     

A planar rod model with flexible cross-section for the folding and the dynamic deployment of tape springs: Improvements and comparisons with experiments

A planar rod model with flexible cross-section has been recently proposed in literature (Guinot et al., 2012). This model is especially suitable for the modeling of tape springs, which develop localized folds due to the flattening of the cross-section. Starting from a complete non-linear elastic shell model, original kinematics assumptions (inspired from the elastica model) have been made to describe the important in-plane changes of the cross-section shape. In the present work, the choice of the position of the rod reference line is discussed. This choice plays an important role in the overall behavior because of the large changes of the cross-section shape. We show that the model published in Guinot et al. (2012) can be improved by considering the centerline as the rod reference line. This enhanced model is then validated through quantitative comparisons with experimental results of dynamic deployments taken from literature.     

Thermo-elastic aspects of dynamic nucleation

In spite of recent progress in our understanding of the absolute stability of elastic phases under loads, the generic presence of metastable configurations and the possibility of their dynamic breakdown remains a major problem in the mechanical theory of phase transitions in solids. In this paper, by considering the simplest one-dimensional model, we study the interplay between inertial and thermal effects associated with nucleation of a new phase, and address the crucial question concerning the size of a perturbation breaking metastability. We begin by reformulating the nucleation problem as a degenerate Riemann problem. By choosing a specific kinetic relation, originating from thermo-visco-capillary (TVC) regularization, we solve a self-similar problem analytically and demonstrate the existence of two types of solutions: with nucleation and without it. We then show that in the presence of a non-zero latent heat, solution with nucleation may by itself be non-unique. To understand the domain of attraction of different self-similar solutions with and without nucleation, we regularize the model and study numerically the full scale initial value problem with locally perturbed data. Through numerical experiments we present evidence that the TVC regularization is successful in removing deficiencies of the classical thermo-elastic model and is sufficient in specifying the limits of metastability.     

Nonlinear transient dynamic response of damped plates using a higher order shear deformation theory

Damped transient dynamic elasto-plastic analysis of plate is investigated. A finite element model based on a C ⁰ higher order shear deformation theory has been developed. Nine noded Lagrangian elements with five degrees of freedom per node are used. Selective Gauss integration is used to evaluate energy terms so as to avoid shear locking and spurious mechanisms. Von Mises and Tresca yield criteria are incorporated along with associated flow rules. Explicit central difference time stepping scheme is employed to integrate temporal equations. The mass matrix is diagonalized by using the efficient proportional mass lumping scheme. A program is developed for damped transient dynamic finite element analysis of elasto-plastic plate. Several numerical examples are studied to unfold different facets of damping of elasto-plastic plates.     

An investigation of the static and dynamic behavior of electrically actuated rectangular microplates

We present an investigation of the static and dynamic behavior of the nonlinear von-Karman plates when actuated by the nonlinear electrostatic forces. The investigation is based on a reduced order model developed using the Galerkin method, which rely on modeshapes and in-plane shape functions extracted using a finite element method. In this study, a fully clamped microplate is considered. We investigate the static behavior and the effect of different non-dimensional design parameters. The static results are validated by comparison with the results calculated by a finite element model. The forced-vibration response of the plate is then investigated when the plate is excited by a harmonic AC load superimposed to a DC load. The dynamic behavior is examined near the primary and secondary (superharmonic and subharmonic) resonances. The microplate shows a strong hardening behavior due to the cubic nonlinearity of mid-plane stretching. However, the behavior switches to softening as the DC load is increased. Finally, near-square plates are studied to understand the effect of geometric imperfections of microplates.     

Formulation of a finite deformation model for the dynamic response of open cell biphasic media

The paper illustrates a biphasic formulation which addresses the dynamic response of fluid saturated porous biphasic media at finite deformations with no restriction on the compressibility of the fluid and of the solid skeleton. The proposed model exploits four state fields of purely kinematic nature: the displacements of the solid phase, the velocity of the fluid, the density of the fluid and an additional macroscopic scalar field, termed effective Jacobian, associated with the effective volumetric deformation of the solid phase.The governing equations are characterized by the property of being all expressed in the reference configuration of the solid phase and by the property of employing only work-conjugate variables, thus avoiding the use of a total Cauchy stress tensor.In particular, the set of governing equations includes a momentum balance equation associated with the effective Jacobian field. This equation, differently from the closure-equations proposed by other authors which express a saturation constraint or a porosity balance, is derived as a stationarity condition on account of a least-action variational principle.