Non-smooth model and numerical analysis of a friction driven structure for piezoelectric motors

In this contribution, typical friction driven structures are summarized and presented considering the mechanical structures and operation principles of different types of piezoelectric motors. A two degree-of-freedom dynamic model with one unilateral frictional contact is built for one of the friction driven structures. Different contact regimes and the transitions between them are identified and analyzed. Numerical simulations are conducted to find out different operation modes of the system concerning the sequence of contact regimes in one steady state period. The influences of parameters on the operation modes and corresponding steady state characteristics are also explored. Some advice are then given in terms of the design of friction driven structures and piezoelectric motors.     

Some considerations on the experimental determination of moments of inertia

The experimental determination of the moments of inertia of rigid bodies, which is a common practice in many fields of technology, is usually performed using torsional or multifilar pendula. Different experimental techniques, based on the study of the periodic or non-periodic motion of the test object on which known forces act, are described and critically analysed. In particular, the effect of damping and, in the case of devices which can be assimilated to a pendulum, that of the non-linearity due to the finite amplitude of the motion, are studied in detail.The equations of motion of the multifilar pendulum are studied in detail to assess how the assumptions usually considered affect the accuracy of the results. An example of experimental determination of the moment of inertia of a flywheel, employing the trifilar pendulum currently used at the Laboratory of the Mechanics Department of Politecnico di Torino, shows how the theoretical considerations apply to a practical case.

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Sommario La determinazione sperimentale dei momenti d'inerzia di corpi rigidi, prassi consueta in molti settori della tecnologia, si avvale normalmente dell'utilizzo di pendoli di torsione o di pendoli multifilari. Nel presente lavoro vengono descritti ed esaminati criticamente vari metodi, basati sullo studio di moti periodici o non periodici dell'oggetto in prova sottoposto a forze note. Viene studiato in particolare l'effetto dello smorzamento e, nel caso di metodi basati su dispositivi assimilabili ad un pendolo, quello delle nonlinearità dovute all'ampiezza delle oscillazioni sui risultati della misura.Vengono studiate in dettaglio le equazioni del moto del pendolo multifilare allo scopo di valutare in quale misura le ipotesi semplificative normalmente accettate influiscano sulla precisione dei risultati. Un esempio di misura sperimentale effettuata mediante il pendolo trifilare correntemente utilizzato presso il laboratorio del Dipartimento di Meccanica del Politecnico di Torino conclude il lavoro e permette di verificare le conclusioni teoriche in un caso concreto.

     

Analysis of wave propagation in piezoelectric coupled cylinder affected by transverse shear and rotary inertia

In this paper, we examine the wave propagation in a piezoelectric coupled cylindrical shell affected by the shear effect and rotary inertia. A complete mathematical analysis of wave propagation solution in this piezoelectric coupled cylindrical shell is provided. The dispersion characteristics are derived through the solving an eigenvalue problem. Results are validated by the classical solution of a metallic cylinder. Besides providing and discussing the dispersion curves for different wave modes, we also examine the piezoelectric effects on the dispersion curves. Further to the above investigation, comparison of dispersion solutions from different shell theories is also conducted. This work may serve as a benchmark for wave propagation in piezoelectric coupled cylindrical shells.     

Nonlinear vibration analysis of piezoelectric bending actuators: Theoretical and experimental studies

Piezoelectric bimorph actuators are used in a variety of applications, including micro positioning, vibration control, and micro robotics. The nature of the aforementioned applications calls for the dynamic characteristics identification of actuator at the embodiment design stage. For decades, many linear models have been presented to describe the dynamic behavior of this type of actuators; however, in many situations, such as resonant actuation, the piezoelectric actuators exhibit a softening nonlinear behavior; hence, an accurate dynamic model is demanded to properly predict the nonlinearity. In this study, first, the nonlinear stress–strain relationship of a piezoelectric material at high frequencies is modified. Then, based on the obtained constitutive equations and Euler–Bernoulli beam theory, a continuous nonlinear dynamic model for a piezoelectric bending actuator is presented. Next, the method of multiple scales is used to solve the discretized nonlinear differential equations. Finally, the results are compared with the ones obtained experimentally and nonlinear parameters are identified considering frequency response and phase response simultaneously. Also, in order to evaluate the accuracy of the proposed model, it is tested out of the identification range as well.     

High-velocity deformation properties of polyurethane foams

This paper presents the results of dynamic uniaxial-stress tests performed on polymer-foam material. A water-blown ester polyurethane foam designated as rigid and a castor-oil-base polyurethane foam designated as semirigid were tested in tension and compression at rates of loading from 10^?3 in./in./sec to 10³ in./in./sec at room temperature. A gas-operated medium-strain-rate machine was used for rates of loading from 10^?3 to about 10² in./in./sec. Tests at higher rates were performed on a split Hopkinson-bar device. Highspeed photographic techniques were used to study dynamic fracture.     

Mechanical energy transductions in standing wave ultrasonic motors: Analytical modelling and experimental investigations

The present work deals with experimental and theoretical analyses of mechanical energy transductions in standing wave ultrasonic motors. A piezoelectric translator prototype previously developed is tested with regard to both out-of-plane and tangential mechanical behaviours. Influences of the vibration amplitude, the normal pre-load and the dynamic friction coefficient at the stator/frame interface are pointed out through the acquisition of speed-driving force characteristics. In the main part of the article, theoretical approaches assuming the decoupling of the out-of-plane and tangential behaviours are proposed: the `complete' model takes into account transient phenomena and tangential inertia effects, and the `simplified' model supposes that the steady state is achieved. In both models, equivalent mass-spring systems allow the intermittent stator/frame contact to be characterized with regard to the vibration amplitude and the normal pre-load. Successive contact and flight periods are clearly shown. During contact periods, the sequences of stick-slip phases are at the origin of the driving mechanism. They are theoretically discriminated through the study of their behaviour equations. Finally, experimental and theoretical data fitting proves the validation of analytical analyses and allows the future optimization of standing wave ultrasonic motors to be envisaged.     

Double rolling isolation systems: A mathematical model and experimental validation

Rolling isolation systems (RISs) protect fragile building contents from earthquake hazards by decoupling horizontal floor motions from the horizontal responses of the isolated object. The RISs in use today have displacement capacities of about 20 cm. This displacement capacity can be increased by stacking two systems. This paper presents and evaluates a complete non-linear model of the coupled dynamics of double RISs. The model is derived through the fundamental form of Lagrange׳s equation and involves the non-holonomic constraints of spheres rolling between non-parallel surfaces. The derivation requires the use of two translating and rotating reference frames. The proposed model is validated through comparisons between experimentally measured and numerically predicted time histories and peak response quantities—total acceleration and relative displacement. The effects of the initial conditions, the mass of the isolated object, and the amplitude and period of the disturbance on the system׳s performance are assessed.     

Influences of large deformation and rotary inertia on wave propagation in piezoelectric cylindrically laminated shells in thermal environment

Influences of large deformation (geometrical non-linear) and rotary inertia on wave propagation in a long, piezoelectric cylindrically laminated shell in thermal environment is presented in this paper. Nonlinear dynamic governing equations of piezoelectric cylindrically laminated shells are derived by means of Hamilton’s principle. The wave propagation modes are obtained by solving an eigenvalue problem. Numerical examples show that the characteristics of wave propagation in piezoelectric cylindrically laminated shells are relates to the large deformation, rotary inertia and thermal environment of the piezoelectric cylindrically laminated shells. The effect of large deformation, rotary inertia and thermal load on wave propagation in the piezoelectric cylindrically laminated shells is discussed by comparing with the result from the small deformation (geometrical linear shell theory). This method may be used to investigate wave propagation in various laminated material, layers numbers and thickness of piezoelectric cylindrically laminated shells under large deformation. The results carried out can be used in the ultrasonic inspection techniques and structural health monitoring.     

Actively compensated aerostatic thrust bearing: design,modelling and experimental validation

Active compensation is an effective method for increasing air bearing static and dynamic performance. This paper describes the design, modelling and experimental validation of an actively compensated externally pressurized gas bearing. The active compensation is obtained through the support compensation strategy. With this strategy, the system’s initial working position is restored by compensating for air gap variations through adjustments to the bearing vertical dimension. The described bearing consists in a conventional thrust bearing which is integrated with a multilayer piezoelectric actuator, a compliant mechanism and a digital controller. Nevertheless the non-linear nature of the air system, a simple linear model results to be an effective choice for neighbour of equilibrium conditions. Results demonstrate the good accuracy of the model and the system’s good capacity of rejecting external force disturbances.     

Dislocation-mediated strain hardening in tungsten: Thermo-mechanical plasticity theory and experimental validation

A self-consistent thermo-mechanical model to study the strain-hardening behavior of polycrystalline tungsten was developed and validated by a dedicated experimental route. Dislocation–dislocation multiplication and storage, as well dislocation-grain boundary (GB) pinning were the major mechanisms underlying the evolution of plastic deformation, thus providing a link between the strain hardening behavior and material's microstructure. The microstructure of the polycrystalline tungsten samples has been thoroughly investigated by scanning and electron microscopy. The model was applied to compute stress–strain loading curves of commercial tungsten grades, in the as-received and as-annealed states, in the temperature range of 500–1000 °C. Fitting the model to the independent experimental results obtained using a single crystal and as-received polycrystalline tungsten, the model demonstrated its capability to predict the deformation behavior of as-annealed samples in a wide temperature range and applied strain. The relevance of the dislocation-mediated plasticity mechanisms used in the model have been validated using transmission electron microscopy examination of the samples deformed up to different amounts of strain. On the basis of the experimental validation, the limitations of the model are determined and discussed.     

Numerical modeling of deposition-release mechanisms in long-term filtration: validation from experimental data

A numerical phenomenological filtration model based on the combination of existing modeling approaches for simulating the transport of suspended particles in saturated porous medium is presented. The model accounts for the decreased physical straining with the distance from the inlet and the amount of deposited particles in the deposition kinetics. The particle release flux is a function of the local shear stress exerted by the flow on the pore surfaces. The proposed model is validated by interpreting a series of experimental data, realized in a laboratory sand column. The results show that the present model allows simulating the presence of a plateau in the breakthrough curves in the light of the shear stress conditions, and the spatial profile of deposited particles in the porous medium in the light of the straining profile.     

动态多稳态压电风能俘能结构设计与实验验证

传统的线性颤振式风能俘能结构在变风速环境下转换效率不高.针对此问题,论文提出了一种动态多稳态颤振式压电俘能结构,可在较宽的风速范围内保持较高的电压输出.该结构在悬臂梁自由端有一矩形平板和一永磁体,并在梁自由端附近放置两个固定永磁体,磁铁间的磁吸力使结构具有两个静态稳定平衡位置和一个动态稳定平衡位置.为了验证所提出结构的优越性,加工了实验装置,开展了不同风速下风能转换效率的研究.发现当风速较小时,该结构具有双稳态特性;而当风速较大时,结构会出现新的稳定位置,变为三稳态系统.利用这种动态多稳态特性,可在很宽的风速范围内实现阱间跳跃并伴随高电压输出.实验结果表明,这种动态多稳态结构,当风速在2.0 m/s-7.5 m/s区间变化时,能够激发并保持阱间跳跃,甚至相干共振.因此,该结构可在宽风速阈环境下保障电能的高效输出.     

An experimental validation of load distribution in screw threads

The thread load distribution has been examined, as is known, in literature both theoretically and experimentally. in the present paper the load distribution is validated by strain-gage measurements. Starting from the theoretical load distribution the stresses on the outer surface of the female member of a threaded connection are calculated. The theoretical and experimental stress values obtained are reasonably close.     

A piezoelectric based energy harvester with dynamic magnification: modelling,design and experimental assessment

This work presents a simple and innovative piezoelectric energy harvester, inspired by fractal geometry and intrinsically including dynamic magnification. Energy harvesting from ambient vibrations exploiting piezoelectric materials is an efficient solution for the development of self-sustainable electronic nodes. After an initial design step, the present work investigates the eigenfrequencies of the proposed harvester, both through a simple free vibration analysis model and through a computational modal analysis. The experimental validation performed on a prototype, confirms the accurate frequency response predicted by these models with five eigenfrequencies below 100 Hz. Despite the harvester has piezoelectric transducers only on a symmetric half of the top surface of the lamina, the rate of energy conversion is significant for all the investigated eigenfrequencies. Moreover, by adding a small ballast mass on the structure, it is possible to excite specific eigenfrequencies and thus improving the energy conversion.     

A microstructural flow-induced crystallization model for film blowing: validation with experimental data

The two-phase microstructural/constitutive model for film blowing of Doufas and McHugh (D-M) (J Rheol 45:1085–1104, 2001a) is validated against online film data of a linear low-density polyethylene (LLDPE) at a variety of processing conditions. The D-M model includes the effects of thermal and flow-induced (enhanced) crystallization (FIC) coupled with the rheological response of both the melt and semicrystalline phases under fabrication conditions. The model predictions of bubble radius, velocity, and crystallinity profiles are in quantitative agreement with available experimental data over a wide range of blow-up ratios (BUR), take-up ratios (TUR), and bubble cooling rates using the same set of material/model parameters. The model naturally predicts the location of the frost line as a consequence of system stiffening due to crystallization overcoming the pitfalls of traditional modeling approaches that impose it as an artificial boundary condition. For a wide range of processing conditions, it is found that key film mechanical properties including elongation to break, yield stress, tensile modulus, and tear strength correlate well with predicted locked-in extensional stresses and molecular orientation at the frost line enabling development of quantitative structure-process-properties relationships that are useful in product and process development. The D-M model for film blowing is physics-based including elements of molecular rheology (polymer kinetic theory), suspension, and nucleation theories as well as irreversible thermodynamics principles, yet being tractable for continuum-based numerical simulations with practical industrial applicability. The FIC enhancement factor of the model is shown to be proportional to $\exp \left (\lambda _{\text {eff},\textnormal {w}}^{2} -1\right )$ , where λ _eff,w is a molecular chain stretch ratio of the whole chain and proportional to exp (λ ² ? 1), where λ is the stretch ratio of the remaining (uncrystallized) amorphous chain, consistent with fundamental kinetic Monte Carlo simulations of flow-induced nucleation of Graham and Olmsted (Phys Rev Lett 103:115702-1–115702-4, 2009).     

Inelastic impact dynamics of ships with one-sided barriers. Part II: experimental validation

This paper is the second part of a two-part study of impact interaction of a ship roll motion with one-sided ice barrier. The first part was devoted to analytical and numerical simulations for the case of inelastic impact. The analytical approach was based on Zhuravlev and Ivanov non-smooth coordinate transformations. Extensive numerical simulations were carried out for all initial conditions covered by the ship grazing orbit for different values of excitation amplitude and frequency of external wave-induced roll moment. The basins of attraction of safe operation revealed the coexistence of different response regimes such as non-impact periodic oscillations, modulated impact motion, period added impact oscillations, chaotic impact motion and roll-over dynamics. This part presents an experimental investigation conducted on a small ship model in a tow tank. In particular, the experimental tests reveal complex dynamic response characteristics such as multi-frequency wave motion caused by the wave reflection from the tank end wall. Measured results show a good agreement with the predicted results by for small angles of the barrier relative to the ship unbiased position. However, deviation becomes significant as the angle increases. This deviation is mainly attributed to the uncertainty of the coefficient of restitution, which is found to depend on the velocity of impact in addition to the geometry and material properties of the model and barrier.