Showing papers on "Inertia published in 2001"

Three Dimensional Absolute Nodal Coordinate Formulation for Beam Elements: Theory

Abstract: The description of a beam element by only the displacement of its centerline leads to some difficulties in the representation of the torsion and shear effects. For instance such a representation does not capture the rotation of the beam as a rigid body about its own axis. This problem was circumvented in the literature by using a local coordinate system in the incremental finite element method or by using the multibody floating frame of reference formulation. The use of such a local element coordinate system leads to a highly nonlinear expression for the inertia forces as the result of the large element rotation. In this investigation, an absolute nodal coordinate formulation is presented for the large rotation and deformation analysis of three dimensional beam elements. This formulation leads to a constant mass matrix, and as a result, the vectors of the centrifugal and Coriolis forces are identically equal to zero. The formulation presented in this paper takes into account the effect of rotary inertia, torsion and shear, and ensures continuity of the slopes as well as the rotation of the beam cross section at the nodal points. Using the proposed formulation curved beams can be systematically modeled.

Inertial effects in suspension and porous-media flows

Abstract: ▪ Abstract The current understanding of the average flow properties of packed beds and particle suspensions, in which inertia plays a significant role on the particle length scale, is examined. The features of inertial suspensions posing challenges to theoriticians include the nonlinear and unsteady nature of the governing equations, the inability to superimpose solutions, the prevalence of hydrodynamic instabilities, and the existence of particle-particle collisions. We discuss two special cases of inertial suspensions, for which detailed kinetic theories have been developed: (a) particles in a gas, and (b) spherical, high-Reynolds number bubbles in liquid. Subsequently, we review recent applications of computational fluid dynamics to simulate the motion in particle suspensions with both inertia and vorticity in the continueous phase. The synthesis of these analytical and numerical techniques is a promising approach to address the many challenges of modelling inertial suspensions.

Intermittent distribution of inertial particles in turbulent flows.

Abstract: We consider inertial particles suspended in an incompressible turbulent flow. Because of particles' inertia their flow is compressible, which leads to fluctuations of concentration significant for heavy particles. We show that the statistics of these fluctuations is independent of details of the velocity statistics, which allows us to predict that the particles cluster on the viscous scale of turbulence and describe the probability distribution of concentration fluctuations. We discuss the possible role of the clustering in the physics of atmospheric aerosols, in particular, in cloud formation.

Three Dimensional Absolute Nodal Coordinate Formulation for Beam Elements: Implementation and Applications

Abstract: This part of these two companion papers demonstrates the computer implementation of the absolute nodal coordinate formulation for three-dimensional beam elements. Two beam elements that relax the assumptions of Euler-Bernoulli and Timoshenko beam theories are developed. These two elements take into account the effect of rotary inertia, shear deformation and torsion, and yet they lead to a constant mass matrix. As a consequence, the Coriolis and centrifugal forces are identically equal to zero. Both beam elements use the same interpolating polynomials and have the same number of nodal coordinates. However, one of the elements has two nodes, while the other has four nodes. The results obtained using the two elements are compared with the results obtained using existing incremental methods. Unlike existing large rotation vector formulations, the results of this paper show that no special numerical integration methods need to be used in order to satisfy the principle of work and energy when the absolute nodal coordinate formulation is used. These results show that this formulation can be used in manufacturing applications such as high speed forming and extrusion problems in which the element cross section dimensions significantly change.

Electroosmotic Flows in Microchannels with Finite Inertial and Pressure Forces

Abstract: Emerging microfluidic systems have spurred an interest in the study of electrokinetic flow phenomena in complex geometries and a variety of flow conditions. This paper presents an analysis of the effects of fluid inertia and pressure on the velocity and vorticity field of electroosmotic flows. In typical on-chip electrokinetics applications, the flow field can be separated into an inner flow region dominated by viscous and electrostatic forces and an outer flow region dominated by inertial and pressure forces. These two regions are separated by a slip velocity condition determined by the Helmholtz-Smoulochowski equation. The validity of this assumption is investigated by analyzing the velocity field in a pressure-driven, two-dimensional flow channel with an impulsively started electric field. The regime for which the inner/outer flow model is valid is described in terms of nondimensional parameters derived from this example problem. Next, the inertial forces, surface conditions, and pressure-gradient conditions for a full-field similarity between the electric and velocity fields in electroosmotic flows are discussed. A sufficient set of conditions for this similarity to hold in arbitrarily shaped, insulating wall microchannels is the following: uniform surface charge, low Reynolds number, low Reynolds and Strouhal number product, uniform fluid properties, and zero pressure differences between inlets and outlets. Last, simple relations describing the generation of vorticity in electroosmotic flow are derived using a wall-local, streamline coordinate system.

High Speed CNC System Design. Part II : Modeling and Identification of Feed Drives

Abstract: Accurate modeling and identification of the feed drives' dynamics is an important step in designing a high performance CNC. This paper presents a method for identifying the dynamic parameters, as well as the friction characteristics of machine tool drives. The inertia and viscous friction are estimated through an unbiased least squares scheme. The friction model is developed by observing the disturbance torque through a Kalman filter, while jogging the axes under closed loop control at various speeds. The overall axis model is used in designing a high speed feed drive control system, which has been presented in Part III of this paper. As verification of the identified friction model, contouring test results without and with friction compensation are also presented.

Adaptive Control of Nonlinear Attitude Motions Realizing Linear Closed Loop Dynamics

Abstract: An adaptive attitude control law is presented that realizes linear closed-loop dynamics in the attitude error vector. The modified Rodrigues parameters (MRPs) are used as the kinematic variables since they are nonsingular for all possible rotations. The desired linear closed-loop dynamics can be of either PD or PID form. Only a crude estimate of the moment of inertia matrix is assumed to be known. An open-loop nonlinear control law is presented which yields linear closed-loop dynamics in terms of the MRPs. An adaptive control law is developed which asymptotically enforces these desired linear closed-loop dynamics in the presence of large inertia and external disturbance model errors. Since the unforced closed-loop dynamics are nominally linear, standard linear control methodologies can be employed to satisfy design requirements. The adaptive control law is shown to track the desired linear performance asymptotically without requiring a priori knowledge of either the inertia matrix or external disturbance.

Equations of motion for a two-axes gimbal system

Abstract: Equations of motion for the two-axes yaw-pitch gimbal configuration are discussed on the assumption that the gimbals are rigid bodies and have no mass unbalance. The equations are derived and different terms are brought together into separate groups for the sake of clarity and to facilitate certain interpretations. Different kinds of disturbances and their elimination or reduction are discussed, as is the yaw gain dependence on the pitch angle. Inertia cross couplings are also given. The purpose is twofold: to simplify the picture of the two-axes gimbals and to further illustrate the properties of this configuration.

Non-linear adaptive robust control of electro-hydraulic systems driven by double-rod actuators

Abstract: This paper studies the high performance robust motion control of electro-hydraulic servo-systems driven by double-rod hydraulic actuators. The dynamics of hydraulic systems are highly non-linear and the system may be subjected to non-smooth and discontinuous non-linearities due to directional change of valve opening, friction and valve overlap. Aside from the non-linear nature of hydraulic dynamics, hydraulic servosystems also have large extent of model uncertainties. To address these challenging issues, the recently proposed adaptive robust control (ARC) is applied and a discontinuous projection based ARC controller is constructed. The resulting controller is able to take into account the effect of the parameter variations of the inertia load and the cylinder hydraulic parameters as well as the uncertain non-linearities such as the uncompensated friction forces and external disturbances. Non-differentiability of the inherent non-linearities associated with hydraulic dynamics is carefully examined and add...

Passive velocity field control (PVFC). Part I. Geometry and robustness

Abstract: Passive velocity field control is a control methodology for fully actuated mechanical systems, in which the motion task is specified behaviorally in terms of a velocity field, and the closed-loop system is passive with respect to a supply rate given by the environment power input The control law is derived geometrically and the geometric and robustness properties of the closed-loop system are analyzed It is shown that the closed-loop unforced trajectories are geodesics of a closed-loop connection which is compatible with an inertia metric, and that the velocity of the system converges exponentially to a scaled multiple of the desired velocity field The robustness property of the system exhibits some strong directional preference In particular, disturbances that push in the direction of the desired momentum do not adversely affect the performance Moreover, robustness property also improves with more energy in the system

Axisymmetric gravity currents in a rotating system: experimental and numerical investigations

Abstract: The propagation at high Reynolds number of a heavy, axisymmetric gravity current of given initial volume over a horizontal boundary is considered in both rotating and non-rotating situations. The investigation combines experiments with theoretical predictions by both shallow-water approximations and numerical solutions of the full axisymmetric equations. Attention is focused on cases when the initial ratio of Coriolis to inertia forces is small. The experiments were performed by quickly releasing a known cylindrical volume of dense salt water of 2 m diameter at the centre of a circular tank of diameter 13 m containing fresh ambient water of typical depth 80 cm. The propagation of the current was recorded for different initial values of the salt concentration, the volume of released fluid, the ratio of the initial height of the current to the ambient depth, and the rate of rotation. A major feature of the rotating currents was the attainment of a maximum radius of propagation. Thereafter a contraction–relaxation motion of the body of fluid and a regular series of outwardly propagating pulses was observed. The frequency of these pulses is slightly higher than inertial, and the amplitude is of the order of magnitude of half the maximum radius. Theoretical predictions of the corresponding gravity currents were also obtained by (i) previously developed shallow-water approximations (Ungarish & Huppert 1998) and (ii) a specially developed finite-difference code based on the full axisymmetric Navier–Stokes equations. The ‘numerical experiments’ provided by this code are needed to capture details of the flow field (such as the non-smooth shape of the interface, the vertical dependence of the velocity field) which are not reproduced by the shallow-water model and are very difficult for, or outside the range of, accurate experimental measurement. The comparisons and discussion provide insight into the flow field and indicate the advantages and limitations of the verified simulation tools.

Dynamic calibration of a wheelchair dynamometer.

Abstract: The inertia and resistance of a wheelchair dynamometer must be determined in order to compare the results of one study to another, independent of the type of device used. The purpose of this study was to describe and implement a dynamic calibration test for characterizing the electro-mechanical properties of a dynamometer. The inertia, the viscous friction, the kinetic friction, the motor back-electromotive force constant, and the motor constant were calculated using three different methods. The methodology based on a dynamic calibration test along with a nonlinear regression analysis produced the best results. The coefficient of determination comparing the dynamometer model output to the measured angular velocity and torque was 0.999 for a ramp input and 0.989 for a sinusoidal input. The inertia and resistance were determined for the rollers and the wheelchair wheels. The calculation of the electro-mechanical parameters allows for the complete description of the propulsive torque produced by an individual, given only the angular velocity and acceleration. The measurement of the electro-mechanical properties of the dynamometer as well as the wheelchair/human system provides the information necessary to simulate real-world conditions.

The effect of the Coriolis force on axisymmetric rotating thin film flows

Abstract: The axisymmetric flow of a thin Newtonian fluid layer subject to centrifugal and Coriolis forces, surface tension and gravity is considered. Employing lubrication theory the mathematical problem is reduced to the solution of a fourth-order nonlinear partial differential equation for the film height, which requires solving numerically. At the moving contact line a precursor film model is adopted. Once the film height is known other quantities, such as fluid velocities and pressure may be easily determined. Of particular interest, is the fact that, within the restrictions of lubrication theory the Coriolis term in the radial velocity equation is of the same order as the inertia terms and is therefore negligible. This means the velocity equations are not fully coupled and, when the flow is axisymmetric, the Coriolis force has no effect on the height of the fluid film.

A gyrokinetic ion zero electron inertia fluid electron model for turbulence simulations

Abstract: This paper describes the formulation of a hybrid model with fully gyrokinetic ions and a zero-inertia fluid model for the electrons. The electron fluid equations are derived from moments of the drift kinetic equation, taking the small mass ratio limit, but with finite electron temperature. This model eliminates the inertial Alfven wave and any physics relating to electron transit motion, making it useful for studying low frequency, high β (β≫me/mi) electromagnetic turbulence as well as kinetic magnetohydradynamics (MHD) physics including kinetic ballooning and toroidal Alfven eigenmodes. Electromagnetic effects (δB⊥) are included through the parallel ion and electron current. A predictor-corrector scheme for the fluid part that is consistent with the gyrokinetic ion part has been developed. Here we derive the model equations, derive the linear kinetic-fluid theory in a three-dimensional shearless slab, and compare the simulation results with the linear theory.

A Simultaneous Numerical Solution for the Lubrication and Dynamic Stability of Noncontacting Gas Face Seals

Abstract: A numerical solution is presented for the dynamic analysis of gas lubricated noncontacting mechanical face seals having a single grounded flexibly mounted stator. Seal dynamics is solved in axial and angular modes of motion. Both the Reynolds equation and the equations of motion are arranged into a single state space form, allowing the fluid film lubrication and the dynamics to be solved simultaneously. The resulting set of equations is solved using a high-order multistep ordinary differential equation solver, yielding a complete simulation for the seal dynamic behavior. Examples of seal motion are given in detailed transient responses. The stability threshold is investigated to gauge the influence of seal parameters such as inertia, speed, coning, and the direction of sealed pressure drops. The results show two modes of instability: (1) When the inertia effect is larger than a critical value, the natural response of the seal grows monotonically in a half-frequencywhirl mode. (2) When the seal coning is less than some critical value in an outside pressurized seal, the minimum film thickness diminishes because of hydrostatic instability, and face contact occurs. Conversely, an inside pressurized seal is shown to be hydrostatically stable and have a superior dynamic response at any coning. @DOI: 10.1115/1.1308020#

The transition from inertia- to bottom-drag-dominated motion of turbulent gravity currents

Abstract: The influence of drag on the motion of gravity currents over rigid horizontal surfaces is considered analytically using a Chezy model of boundary shear stress. Although the initial motion is governed by a balance between the buoyancy forces and fluid inertia, drag gradually influences the flow. The length and time scales at which these effects become significant are identified. A perturbation series, valid at early times, is constructed to analyse the changes to the velocity and height of the evolving current due to drag. At much later times, a new class of similarity solutions is developed to model the motion which is now governed by a balance between buoyancy and drag. The transition in the dominant forces which govern the dynamics of the flow is examined by numerically integrating the equations of motion for flows generated by a constant flux of relatively dense fluid. The numerical results confirm both the perturbation solution, valid at early times, and the new similarity solution valid at late times. The transition between the two may involve the formation of a discontinuity (bore). Finally particle-driven currents, which exhibit different dynamical behaviour due to the progressive reduction of their density arising from particle sedimentation, are investigated.

Motion of a drop in a vertical temperature gradient at small Marangoni number the critical role of inertia

Abstract: When a drop moves in a uniform vertical temperature gradient under the combined action of gravity and thermocapillarity at small values of the thermal Peclet number, it is shown that inclusion of inertia is crucial in the development of an asymptotic solution for the temperature field. If inertia is completely ignored, use of the method of matched asymptotic expansions, employing the Peclet number (known as the Marangoni number) as the small parameter, leads to singular behaviour of the outer temperature field. The origin of this behaviour can be traced to the interaction of the slowly decaying Stokeslet, arising from the gravitational contribution to the motion of the drop, with the temperature gradient field far from the drop. When inertia is included, and the method of matched asymptotic expansions is used, employing the Reynolds number as a small parameter, the singular behaviour of the temperature field is eliminated. A result is obtained for the migration velocity of the drop that is correct to O(Re 2 log Re)

Somatosensory attunement to the rigid body laws.

Abstract: In the most general case, haptic perception of an object's heaviness is most likely the perception of the object's resistance to movement, determined jointly by the object's mass and mass distribution. In two experiments with occluded objects wielded freely in three dimensions, we showed additive effects on perceived heaviness of mass and the inertia tensor. Our manipulations of the inertia tensor were directed specifically at the volume and symmetry of the inertia ellipsoid, quantities that can be understood as important to controlling the level and patterning of muscular forces, respectively. Ellipsoid volume and symmetry were found to have separate effects on perceptual reports of heaviness that were invariant over different tensors. Independent sensitivities to translational inertia and particular characterizations of rotational inertia suggest specialized somatosensory attunement to the rigid body laws.

Coordinated control of the Zero Inertia Powertrain

Abstract: • A submitted manuscript is the author's version of the article upon submission and before peer-review. There can be important differences between the submitted version and the official published version of record. People interested in the research are advised to contact the author for the final version of the publication, or visit the DOI to the publisher's website. • The final author version and the galley proof are versions of the publication after peer review. • The final published version features the final layout of the paper including the volume, issue and page numbers.

Coupled torsion-lateral stability of a shaft-disk system driven through a universal joint

Abstract: Understanding the instability phenomena of rotor-shaft and driveline systems incorporating universal joints is becoming increasingly important because of the trend towards light-weight, high-speed supercritical designs. In this paper, a nondimensional, periodic, linear time-varying model with torsional and lateral degrees-of-freedom is developed for a rotor shaft-disk assembly supported on a flexible bearing and driven through a U-joint. The stability of this system is investigated utilizing Floquet theory. It is shown that the interaction between torsional and lateral dynamics results in new regions of parametric instability that have not been addressed in previous investigations. The presence of load inertia and misalignment causes dynamic coupling of the torsion and lateral modes, which can result in torsion-lateral instability for shaft speeds near the sum-type combinations of the torsion and lateral natural frequencies. The effect of angular misalignment, static load-torque, load-inertia, lateral frequency split, and auxiliary damping on the stability of the system is studied over a range of shaft operating speeds. Other than avoiding the unstable operating frequencies, the effectiveness of using auxiliary lateral viscous damping as a means of stabilizing the system is investigated. Finally, a closed-form technique based on perturbation expansions is derived to determine the auxiliary damping necessary to stabilize the system for the least stable case (worst case). ©2002 ASME

Design of high speed planar parallel manipulator and multiple simultaneous specification control

Abstract: This paper presents a planar parallel mechanism which can achieve very rapid motion due to the low inertia of its moving parts and the use of multiple simultaneous specification (MSS) control. The proposed parallel manipulator was designed based on a prismatic-revolute-revolute kinematic structure. The proximal prismatic joints were realized using a linear slider with a ball screw mechanism. All actuators remain stationary resulting in a reduction of the inertia of moving parts. Since coupling terms between multiple chains of the parallel manipulator were significant, the MSS control scheme was implemented to satisfy multiple conflicting closed-loop performance specifications. Simulation and experimental results show that the proposed planar parallel manipulator yields better dynamic performance than a conventional X-Y table and has great potential in application to high speed assembly.

Development of a measurement robot for identifying all inertia parameters of a rigid body in a single experiment

Abstract: Standard experiments for identifying inertia parameters of a rigid body only provide a subset of its ten inertia parameters. All of these procedures only use a subset of the information included in the equations of motion of a rigid test body. This application paper discusses the construction and functioning of a laboratory setup (inertia measurement robot) that simultaneously estimates the ten inertia parameters of a rigid body using the complete information hidden in the nonlinear model equations of the test body. The measurement robot has been carefully designed to keep disturbances of the estimation process small. A key construction means to exclude disturbance forces and torques from the measurement chain is to attach a test body to the robot by means of a force-moment sensor. The task has been solved in several steps: mathematical modeling of the spatial equations of motion of a rigid body, representation of the model equations in a form suitable for experimental identification of the ten inertia parameters and for inverse computer simulation of the test body, special design of the measurement robot, experimental analysis, corrections and accuracy test of the force-moment sensor, laboratory experiments for providing test data, and estimation of the inertia parameters. The ten inertia parameters of rigid bodies obtained by the above approach are sufficiently accurate to be used in various applications of industrial practice.

Stage apparatus, vibration control method and exposure apparatus

Abstract: A vibration control method of a stage apparatus having a main stage body that is driven over a base plate, which controls vibration by providing a force to the base plate. The position of a center of gravity and a position of a major inertia axis of the stage apparatus is detected when vibration is applied to the base plate, and the force is controlled based on the detected position of the center of gravity and the major inertia axis. As a result, in this vibration control method, force is controlled based on the actual position of the center of gravity and the major inertia axis, which is determined when vibration is applied to the base plate of actual equipment or by simulation rather than based on the position of the center of gravity and the major inertia axis in a design model. Hence, residual vibration of the base plate is effectively controlled.