Showing papers on "Inertia published in 2004"

First steps in the spreading of a liquid droplet.

Abstract: We describe the first steps of spreading of a liquid droplet brought in contact with a solid that it wets completely. Usually, it is assumed that the dynamics of the droplet results from a balance between the spreading forces and viscosity. But before this classical stage, inertia resists to the motion, which leads to a very different dynamic law. We study experimentally the nature of this law, compare our results with recent theoretical predictions, and determine the duration of this inertial regime.

The effect of advance ratio on the aerodynamics of revolving wings.

Abstract: Recent studies have demonstrated that a quasi-steady model closely matches the instantaneous force produced by an insect wing during hovering flight. It is not clear, however, if such methods extend to forward flight. In this study we use a dynamically scaled robotic model of the fruit fly Drosophila melanogaster to investigate the forces produced by a wing revolving at constant angular velocity while simultaneously translating at velocities appropriate for forward flight. Because the forward and angular velocities were constant wing inertia was negligible, and the measured forces can be attributed to fluid dynamic phenomena. The combined forward and revolving motions of the wing produce a time-dependent free-stream velocity profile, which suggests that added mass forces make a contribution to the measured forces. We find that the forces due added mass make a small, but measurable, component of the total force and are in excellent agreement with theoretical values. Lift and drag coefficients are calculated from the force traces after subtracting the contributions due to added mass. The lift and drag coefficients, for fixed angle of attack, are not constant for non-zero advance ratios, but rather vary in magnitude throughout the stroke. This observation implies that modifications of the quasi-steady model are required in order to predict accurately the instantaneous forces produced during forward flight. We show that the dependence of the lift and drag coefficients upon advance ratio and stroke position can be characterized effectively in terms of the tip velocity ratio – the ratio of the chordwise components of flow velocity at the wing tip due to translation and revolution. On this basis we develop a modified quasi-steady model that can account for the varying magnitudes of the lift and drag coefficients. Our model may also resolve discrepancies in past measurements of wing performance based on translational and revolving motion.

Pull-in Dynamics of an Elastic Beam Actuated by Continuously Distributed Electrostatic Force

Abstract: A detailed study of the transient nonlinear dynamics of an electrically actuated micron scale beam is presented. A model developed using the Galerkin procedure with normal modes as a basis accounts for the distributed nonlinear electrostatic forces, nonlinear squeezed film damping, and rotational inertia of a mass carried by the beam. Special attention is paid to the dynamics of the beam near instability points. Results generated by the model and confirmed experimentally show that nonlinear damping leads to shrinkage of the spatial region where stable motion is realizable. The voltage that causes dynamic instability, in turn, approaches the static pull-in value.

A passivity based Cartesian impedance controller for flexible joint robots - part I: torque feedback and gravity compensation

Abstract: In this paper a novel approach to the Cartesian impedance control problem for robots with flexible joints is presented. The proposed controller structure is based on simple physical considerations, which are motivating the extension of classical position feedback by an additional feedback of the joint torques. The torque feedback action can be interpreted as a scaling of the apparent motor inertia. Furthermore the problem of gravity compensation is addressed. Finally, it is shown that the closed loop system can be seen as a feedback interconnection of passive systems. Based on this passivity property a proof of asymptotic stability is presented.

On the general scaling theory for electrospraying

Abstract: A systematic dimensional rationale is proposed here to analyse the electrohydro-dynamic equations governing liquid electrospraying phenomena in the well-known steady cone-jet mode with no ambient discharges. As a result, a general, unified description of the complete parametrical space for the emitted current and droplet size is given. Four main distinct subspaces, their relevant boundaries and corresponding scaling laws are identified. Laws already proposed fit in their appropriate region, and previously unknown laws are found. A closed solution for the electric current I when inertia and polarization forces dominate is obtained, in agreement with published experimental results.

Compact models for squeezed-film dampers with inertial and rarefied gas effects

Abstract: A modified Reynolds equation where the gas inertia effect is included is derived from the Navier–Stokes equation. Continuum and slip-flow regions are modelled. Small flow velocity is assumed, and border effects are not considered. By introducing an effective flow rate coefficient including the inertial and rare gas effects, existing linearized analytic squeezed-film damping models can be reused. Equivalent-circuit mechanical impedance and admittance implementations for a rectangular parallel-plate damper are given. The model response is compared against 2D and 3D FEM time-domain and frequency-domain simulations with an excellent agreement. The validity and limitations of the models are discussed extensively.

The dynamics of lead-screw drives: Low-order modeling and experiments

Abstract: The closed-loop performance of a lead-screw drive is usually limited by a resonance in which the carriage oscillates in the direction of motion as the screw undergoes longitudinal and torsional deformation. In this paper, we develop a model of lead-screw system dynamics that accounts for the distributed inertia of the screw and the compliance and damping of the thrust bearings, nut, and coupling. The distributed-parameter model of the lead-screw drive system is reduced to a low-order model using a Galerkin procedure and verified by experiments performed on a pair of ball-screw systems. The model is found to accurately predict the presence of a finite right-half plane zero in the transfer function from motor torque to carriage position. A viscoelastic damper incorporated into one of the lead-screw support bearings is shown to give rise to significant, deterministic damping in the system transfer functions.

On the general scaling theory for electrospraying

Abstract: A systematic dimensional rationale is proposed here to analyse the electrohydro-dynamic equations governing liquid electrospraying phenomena in the well-known steady cone-jet mode with no ambient discharges. As a result, a general, unified description of the complete parametrical space for the emitted current and droplet size is given. Four main distinct subspaces, their relevant boundaries and corresponding scaling laws are identified. Laws already proposed fit in their appropriate region, and previously unknown laws are found. A closed solution for the electric current I when inertia and polarization forces dominate is obtained, in agreement with published experimental results.

A novel generic model at asperity level for dry friction force dynamics

Abstract: This paper presents a theoretical model for (dry, low-velocity, wear-less) friction force dynamics based on asperity interaction considerations subject to the phenomenological mechanisms of creep/relaxation, adhesion and (elasto-plastic) deformation in their most generalized forms. The model simulates the interaction of a large population of idealized, randomly distributed asperities with arbitrarily chosen geometrical and elastic properties. Creep and adhesion are simulated by an expedient local coefficient of friction that increases with time of contact, while deformation effects are accounted for by rate-independent hysteresis losses occurring in the bulk of the material of an asperity that is breaking loose. An energy method is adopted to calculate the instantaneous, local friction force leading to better insight into the problem as well as higher numerical efficiency. The results obtained by this model show both qualitative and quantitative agreement with the known types and facets of friction force dynamic behaviour; in particular, pre-sliding quasi time-independent frictional hysteresis in the displacement, velocity weakening, slider “lift-up” effect and frictional lag, in addition to the influence of the various process parameters, all in a single formulation, such as no extant friction model could show before. Moreover, the model is still open for and capable of further refinement and elaboration so as to incorporate local inertia and viscous effects and thus to be extended to include velocity strengthening and lubricated rough contacts.

Theory and design of an orthotic device for full or partial gravity-balancing of a human leg during motion

Abstract: Gravity balancing is often used in industrial machines to decrease the required actuator efforts during motion. In the literature, a number of methods have been proposed for gravity balancing that include counterweights, springs, and auxiliary parallelograms that determine the center of mass. However, these concepts have not yet been seriously applied to rehabilitation machines. This paper presents the underlying theory and design of an orthosis for the human leg that can fully or partially balance the human leg over the range of its motion. This design combines the use of auxiliary parallelograms to determine the center of mass along with springs to achieve a full or partial gravity balanced orthosis design. A first prototype has been constructed to demonstrate the effectiveness of the idea. Future prototypes will have parameters that will be tuned to the geometry and inertia of a human subject and be tailored to an individual's needs.

The evolution of inertia

Abstract: This article examines some evolutionary consequences of architectural inertia in organizations. The main theorem holds that selection favors architectural inertia in the sense that the median level of inertia in a closed population of organizations increases over time. The other key theorems hold that the selection intensity favoring architectural inertia increases with the levels of intricacy and structural opacity and decreases with cultural asperity.

Which mechanical invariants are associated with the perception of length and heaviness of a nonvisible handheld rod? Testing the inertia tensor hypothesis.

Abstract: It has been suggested that the inertia tensor governs many instances of haptic perception. However, the evidence is inconclusive because other candidate mechanical parameters (i.e., invariants) were not or were insufficiently controlled for in pertinent experiments. By independently varying all candidate mechanical parameters, the authors were able to test the role of the inertia tensor relative to that of other mechanical parameters. The results showed that length perception during rod wielding is not governed by the inertia tensor alone but also by the static moment. In contrast to previous reports, length perception during rod holding and heaviness perception during rod wielding were found to be unrelated to the inertia tensor and strongly related to the static moment.

Entropy production of Brownian macromolecules with inertia.

Abstract: We investigate the nonequilibrium steady-state thermodynamics of single Brownian macromolecules with inertia under feedback control in an isothermal ambient fluid. With the control being represented by a velocity-dependent external force, we find such an open system can have a negative entropy production rate, and we develop a mesoscopic theory consistent with the second law. We propose an equilibrium condition and define a class of external force, which includes the transverse Lorentz force, leading to equilibrium.

Improvement of low speed operation of electric machine with an inertia identification using ROELO

Abstract: A new scheme to estimate the moment of inertia in the motor drive system in very low speed is proposed. The simple speed estimation scheme, which is used in most servo systems for low-speed operation, is sensitivity to variations in machine parameters especially the moment of inertia. To estimate the motor inertia value, a reduced-order extended Luenberger observer (ROELO) is applied. The effectiveness of the proposed ROELO is verified by simulation and experiment.

Nonmonotonic velocity dependence of atomic friction.

Abstract: We propose a theoretical model for friction force microscopy experiments with special emphasis on the realistic description of dissipation and inertia effects. Its main prediction is a nonmonotonic dependence of the friction force upon the sliding velocity of the atomic force microscope tip relative to an atomically flat surface. The region around the force maximum can be approximately described by a universal scaling law and should be observable under experimentally realistic conditions.

Dynamics of Electrorheological Suspensions Subjected to Spatially Nonuniform Electric Fields

Abstract: A numerical method based on the distributed Lagrange multiplier method (DLM) is developed for the direct simulation of electrorheological (ER) liquids subjected to spatially nonuniform electric field. The flow inside particle boundaries is constrained to be rigid body motion by the distributed Lagrange multiplier method and the electrostatic forces acting on the particles are obtained using the point-dipole approximation. The numerical scheme is verified by performing a convergence study which shows that the results are independent of mesh and time step sizes. The dynamical behavior of ER suspensions subjected to nonuniform electric field depends on the solids fraction, the ratio of the domain size and particle radius, and four additional dimensionless parameters which respectively determine the importance of inertia, viscous, electrostatic particle-particle interaction and dielectrophoretic forces. For inertia less flows a parameter defined by the ratio of the dielectrophoretic and viscous forces, determines the time duration in which the particles collect near either the local maximums or local minimums of the electric field magnitude, depending on the sign of the real part of the Clausius-Mossotti factor

Dynamics of inertia dominated binary drop collisions

Abstract: A head-on impact of two equal drops is studied theoretically. The initial drops deformation, the radial expansion of the obtained liquid mass, and the subsequent axial stretching are considered. The deformation of the drop in the radial direction is governed by the motion of a rim bounding an expanding lamella, whereas the axial deformation of the drop is governed by the motion of two globules formed at the ends of a stretching liquid jet. The equations of motion of the rim and of the globules are obtained from the mass and the momentum balance. The theory accounts for the inertial effects, surface tension and the viscous stresses. The theoretical predictions of the drop diameter and its length are compared with experiments. The agreement is rather good in spite of the fact that no adjustable parameters are used.

Triaxial rotor model for nuclei with independent inertia and electric quadrupole tensors

Abstract: The triaxial rotor model for nuclei is investigated by relaxing the use of irrotational moments of inertia. The dependence of observables of the model on the electric quadrupole tensor, through a triaxiality angle $(\ensuremath{\gamma})$, and on the inertia tensor, through a mixing angle, is illustrated. This formalism provides insights into the physics of triaxial rotations in nuclei.

Aeroelastic effects of large blade deflections for wind turbines

Abstract: The objective of the present work is to present the latest results in effects of including large blade deflections in aeroelastic calculations and to quantify the errors of the linearized approach for a modern flexible mega-watt sized turbine. In this paper three nonlinear approaches have been used to quantify the effects of large deflections. One approach is a rather simple extension of the already existing aeroelastic code HAWC, which changes the calculation basis so that small deflections are assumed around an initially large deflected blade shape. The second approach is based on a multibody formulation of the beam element used in HAWC, where nonlinear effects are included as a result of modelling the blade using several interconnected bodies. The third approach is a corotational finite element formulation where each element can be regarded as linear and the nonlinear effects are included by translation and rotation of the local element coordinate system. The results from the three nonlinear approaches are compared with results obtained by the existing HAWC, and the impact on the following main effects (due to large deflections) are addressed: 1. The reduction of the effective radius. 2. The reduction of power production due to the reduced effective radius. 3. The effect of increased torsional inertia of the blade due to the deflected shape. 4. The change of blade frequencies due to changes in inertia and coupling effects.

Analysis and Improvement of Particle Swarm Optimization Algorithm

Abstract: The effects of inertia weight on particle swarm optimization (PSO) performance are analyzed. A novel method of selecting inertia weight in PSO is developed, which can tune the expectations of inertia weights adaptively when the inertia weights are randomly selected and lead to effectively balance between the local and global search ability. Results of the two benchmark functions indicate that the PSO algorithm based on the strategy of random inertia weight (RIW) has been significantly improved on both optimization speed and computational accuracy.

Control Authority of a Projectile Equipped With an Internal Unbalanced Part

Abstract: A key technical challenge for smart weapon developers is the design of appropriate control mechanisms that provide sufficient control authority to enable correction of typical trajectory errors while not excessively burdening the overall weapon design. The work reported here considers a rotating mass unbalance control mechanism, created by radial orientation of an internal part. To investigate the potential of this control mechanism, a seven degree-of-freedom flight dynamic model of a projectile, equipped with an internal part is defined. Using this dynamic model it is shown that by holding the internal part fixed with respect to a nonrolling reference frame, predictable trajectory changes are generated including predictable impact point changes. As expected, when unbalance-offset distance, or mass is increased, control authority increases proportionally. This control mechanism creates impact point changes that are the same order of magnitude as dispersion caused by errors induced at launch and in flight. Control authority is significantly altered with changing projectile characteristics, such as, the mass center location, pitch inertia, yaw inertia, aerodynamic drag, and aerodynamic normal force.

Effect of inertia on the Marangoni instability of two-layer channel flow, Part II: normal-mode analysis

Abstract: The effect of inertia on the Yih–Marangoni instability of the interface between two liquid layers in the presence of an insoluble surfactant is assessed for shear-driven channel flow by a normal-mode linear stability analysis. The Orr–Sommerfeld equation describing the growth of small perturbations is solved numerically subject to interfacial conditions that allow for the Marangoni traction. For general Reynolds numbers and arbitrary wave numbers, the surfactant is found to either provoke instability or significantly lower the rate of decay of infinitesimal perturbations, while inertial effects act to widen the range of unstable wave numbers. The nonlinear evolution of growing interfacial waves consisting of a special pair of normal modes yielding an initially flat interface is analysed numerically by a finite-difference method. The results of the simulations are consistent with the predictions of the linear theory and reveal that the interfacial waves steepen and eventually overturn under the influence of the shear flow.

Effect of Inertia and Elasticity on Stick-Slip Motion

Abstract: A hybrid simulation method is used to study the transition from stick-slip motion to steady sliding as the sliding velocity increases above a critical value v(c). The effects of the geometry, elasticity, and mass M of the sliding object are varied to test competing theories. When the slider has a tapered geometry, v(c) scales as M(-1/2), and the elasticity of the slider is irrelevant. When the slider has a constant columnar cross section, elasticity dominates, and v(c) is independent of mass as M--> infinity. The tapered geometry is more typical of existing measurements, but the columnar geometry could be realized using a nanotube.

Similarity solutions for breakup of jets of power law fluids

Abstract: We compute similarity solutions for the breakup of a jet of a power law liquid surrounded by a vacuum. As is known from the Newtonian case, such similarity solutions are fundamentally different depending on whether creeping flow or flow with inertia is considered. We shall investigate both cases. For flow with inertia, we start with Eggers’ solution for the Newtonian case, and we continue it to other values of the power law exponent. The jet profile corresponding to Eggers’ solution is highly asymmmetric. We find that the degree of asymmetry decreases as we deviate from the Newtonian case in either direction. For small as well as for large values of the power law exponent, we find new branches of symmetric solutions. These branches establish a connection between the similarity solutions with and without inertia.

Flux Capacitors and the Origin of Inertia

Abstract: The explanation of inertia based on “Mach's principle” is briefly revisited and an experiment whereby the gravitational origin of inertia can be tested is described. The test consists of detecting a small stationary force with a sensitive force sensor. The force is presumably induced when a periodic transient Mach effect mass fluctuation is driven in high voltage, high energy density capacitors that are subjected to 50 kHz, 1.3 kV amplitude voltage signal, and threaded by an alternating magnetic flux of the same frequency. An effect of the sort predicted is shown to be present in the device tested. It has the expected magnitude and depends on the relative phase of the Mach effect mass fluctuation and the alternating magnetic flux as expected. The observed effect also displays scaling behaviors that are unique to Mach effects. Other tests for spurious signals suggest that the observed effect is real.