Showing papers on "Inertia published in 2000"

Adaptive robust motion control of single-rod hydraulic actuators: theory and experiments

Abstract: High-performance robust motion control of single-rod hydraulic actuators with constant unknown inertia load is considered. The two chambers of a single-rod actuator have different areas, so the dynamic equations describing the pressure changes in them cannot be combined into a single load pressure equation. This complicates controller design since it not only increases the system dimension but also brings in the stability issue of the added internal dynamics. A discontinuous projection-based adaptive robust controller (ARC) is constructed. The controller takes into account not only the effect of parameter variations coming from the inertia load and various hydraulic parameters but also the effect of hard-to-model nonlinearities such as uncompensated friction forces and external disturbances. It guarantees a prescribed output tracking transient performance and final tracking accuracy in general while achieving asymptotic output tracking in the presence of parametric uncertainties. In addition, the zero error dynamics for tracking any nonzero constant velocity trajectory is shown to be globally uniformly stable. Experimental results are obtained for the swing motion control of a hydraulic arm and verify the high-performance nature of the proposed strategy. In comparison to a state-of-the-art industrial motion controller, the proposed algorithm achieves more than a magnitude reduction of tracking errors. Furthermore, during the constant velocity portion of the motion, it reduces the tracking errors almost down to the measurement resolution level.

Speed control of two-inertia system by PI/PID control

Abstract: The purpose of this paper is to develop systematic analysis and design methods for a two-inertia system. A conventional proportional-integral speed control system with a torsional load is redesigned, and the damping characteristic of the system is derived and analyzed. It is shown that the dynamic characteristic of the system strongly depends on the inertia ratio of load to motor. Three kinds of typical pole assignments with identical radius/damping coefficient/real part are applied and compared, and the merits of each pole-assignment design are concluded. Furthermore, for small inertia ratio, we present how to improve the damping of the system by a derivative feedback of motor speed.

Energetics and Stability of Translating Media with an Arbitrarily Varying Length

Abstract: The linear dynamics of a class of translating media with an arbitrarily varying length is investigated. The tension in the media arising from their longitudinal accelerations is incorporated. The dynamic stability of the continuous media relative to the inertial and moving coordinate systems is studied from the energy standpoint. The exact expressions for the rates of change of energies of media are derived and interpreted from both control volume and system viewpoints. The stability analyses relative to the inertial and moving coordinate systems result in the same predictions. Examples including a robotic arm through a prismatic joint and an elevator cable in a high-rise building illustrate the analysis. In particular, the results explain an inherent unstable shortening cable behavior encountered in elevator industry.

The dynamics and scaling law for particles suspended in shear flow with inertia

Abstract: The effect of inertia on the dynamics of a solid particle (a circular cylinder, an elliptical cylinder, and an ellipsoid) suspended in shear flow is studied by solving the discrete Boltzmann equation. At small Reynolds number, when inertia is negligible, the behaviour of the particle is in good agreement with the creeping flow solution showing periodic orbits. For an elliptical cylinder or an ellipsoid, the results show that by increasing the Reynolds number, the period of rotation increases, and eventually becomes infinitely large at a critical Reynolds number, Rec. At Reynolds numbers above Rec, the particle becomes stationary in a steady-state flow. It is found that the transition from a time-periodic to a steady state is through a saddle-node bifurcation, and, consequently, the period of oscillation near this transition is proportional to [mid ]p−pc[mid ]−1/2, where p is any parameter in the flow, such as the Reynolds number or the density ratio, which leads to this transition at p = pc. This universal scaling law is presented along with the physics of the transition and the effect of the inertia and the solid-to-fluid density ratio on the dynamics. It is conjectured that this transition and the scaling law are independent of the particle shape (excluding body of revolution) or the shear profile.

The independent effects of gravity and inertia on running mechanics

Abstract: It is difficult to distinguish the independent effects of gravity from those of inertia on a running animal. Simply adding mass proportionally changes both the weight (gravitational force) and mass (inertial force) of the animal. We measured ground reaction forces for eight male humans running normally at 3 m s -1 and under three experimental treatments: added gravitational and inertial forces, added inertial forces and reduced gravitational forces. Subjects ran at 110, 120 and 130 % of normal weight and mass, at 110, 120 and 130 % of normal mass while maintaining 100 % normal weight, and at 25, 50 and 75 % of normal weight while maintaining 100 % normal mass. The peak active vertical forces generated changed with weight, but did not change with mass. Surprisingly, horizontal impulses changed substantially more with weight than with mass. Gravity exerted a greater influence than inertia on both vertical and horizontal forces generated against the ground during running. Subjects changed vertical and horizontal forces proportionately at corresponding times in the step cycle to maintain the orientation of the resultant vector despite a nearly threefold change in magnitude across treatments. Maintaining the orientation of the resultant vector during periods of high force generation aligns the vector with the leg to minimize muscle forces. Summary

Minimum Time Manoeuvring: The Significance of Yaw Inertia

Abstract: A formal method for the evaluation of the minimum time vehicle manoeuvre is described The problem is treated as one of Optimal Control and is solved using a direct transcription method The resulting Non Linear Programming problem is solved using a Sequential Quadratic Programming (SQP) algorithm for constrained minimisation of a multivariable function The optimisation program is used to investigate the effect of the yaw moment of inertia on vehicle performance in a double lane change manoeuvre The method is shown to have excellent capabilities to predict the vehicle maximum performance in transient conditions and to perform sensitivity analysis The influence of yaw inertia on the minimum manoeuvre time is found to be surprisingly small The extension of the method to larger problems, eg, lap time simulation, is also discussed

Linear Dynamics of an Elastic Beam Under Moving Loads

Abstract: The dynamic response of an Euler-Bernoulli beam under moving loads is studied by mode superposition. The inertial effects of the moving load are included in the analysis. The time-dependent equations of motion in modal space are solved by the method of multiple scales. Instability regions of parametric resonance are identified and the moving mass effect is shown to significantly affect the transient response of the beam. Importance of modal interaction arising out of the possible internal resonance is highlighted. While the external resonance is due to the gravity effects of the moving load, the parametric and internal resonance solely depends on the load mass parameter-ratio of the moving load mass to the beam mass. Numerical results show the influence of the load inertia terms on the beam response under either a single moving load or a series of moving loads.

An effective two-dimensional model for MHD flows with transverse magnetic field

Abstract: This paper presents a model for quasi-two-dimensional MHD flows between two planes with small magnetic Reynolds number and constant transverse magnetic field orthogonal to the planes. A method is presented that allows three-dimensional effects to be taken into account in a two-dimensional equation of motion thanks to a model for the transverse velocity profile. This model is obtained by using a double perturbation asymptotic development both in the core flow and in the Hartmann layers arising along the planes. A new model is thus constructed that describes inertial effects in these two regions. Two separate classes of phenomena are found: one related to inertial effects in the Hartmann layer gives a model for recirculating flows and the other introduces the possibility of having a transverse dependence of the velocity profile in the core flow. The ‘recirculating’ velocity profile is then introduced in the transversally averaged equation of motion in order to provide an effective two-dimensional equation of motion. Analytical solutions of this model are obtained for two experimental configurations: isolated vortices generated by a point electrode and axisymmetric parallel layers occurring in the MATUR (MAgneticTURbulence) experiment. The theory is found to give a satisfactory agreement with the experiment so that it can be concluded that recirculating flows are actually responsible for both vortex core spreading and excessive dissipative behaviour of the axisymmetric sidewall layers.

Synchronization in populations of globally coupled oscillators with inertial effects

Abstract: A model for synchronization of globally coupled phase oscillators including "inertial" effects is analyzed. In such a model, both oscillator frequencies and phases evolve in time. Stationary solutions include incoherent (unsynchronized) and synchronized states of the oscillator population. Assuming a Lorentzian distribution of oscillator natural frequencies, g(Omega), both larger inertia or larger frequency spread stabilize the incoherent solution, thereby making it harder to synchronize the population. In the limiting case g(Omega)=delta(Omega), the critical coupling becomes independent of inertia. A richer phenomenology is found for bimodal distributions. For instance, inertial effects may destabilize incoherence, giving rise to bifurcating synchronized standing wave states. Inertia tends to harden the bifurcation from incoherence to synchronized states: at zero inertia, this bifurcation is supercritical (soft), but it tends to become subcritical (hard) as inertia increases. Nonlinear stability is investigated in the limit of high natural frequencies.

Fluid dynamics. Turbulence without inertia

Abstract: Turbulence is normally driven by fluid inertia (or momentum). But turbulent patterns can be seen in fluids with no inertial forces, if there are high elastic forces. Such patterns may be dubbed ‘elastic turbulence’.

The derivation of a nonlinear filtration law including the inertia effects via homogenization

Abstract: R esum e. On consid ere l' ecoulement stationnaire d'un uide newtonien visqueux incompressible dans un milieu poreux rigide. Pour une structure g eom etrique p eriodique du milieu poreux form ee de cellules carr ees avec des c^ ot es de longueur ", la m ethode d'homog en eisation donne dii erents r esultats selon la relation en-tre ", le nombre de Reynolds et le nombre de Froude. Si le nombre de Reynolds et l'inverse du nombre de Froude sont d'ordre 1=", l' etude asymptotique formelle conduit a un syst eme homog en eis e du type Navier-Stokes a double pression, qui contient une loi nonlocale r egissant la ltration nonlin eaire. En supposant que les donn ees ne sont pas trop grandes, on d emontre que le probl eme homog en eis e poss ede une unique solution r eguli ere. De plus, on montre la convergence du pro-cessus d'homog en eisation et on etablit une estimation d'erreur. Abstract. We consider the stationary viscous incompressible uid ow through a rigid porous medium. For a periodic porous medium, with the period ", the ho-mogenization method gives diierent results depending on the relationship between the Reynolds number, the Froude's number and the period. If both, the Reynolds number and the inverse of the Froude's number are of order 1=", then the formal asymptotic expansion gives a homogenized system containing the fast and slow variables named Navier-Stokes system with two pressures. More precisely the l-tration law is nonlocal and nonlinear. Supposing that the data are not too large we prove the existence of a unique smooth solution for the homogenized problem. Furthermore, the convergence of the homogenization process is proved and the 1 error estimate is established.

Inertial sensor and method of use

Abstract: The inertial sensor of the present invention utilizes a proof mass suspended from spring structures forming a nearly degenerate resonant structure into which a perturbation is introduced, causing a split in frequency of the two modes so that the mode shape become uniquely defined, and to the first order, remains orthogonal. The resonator is provided with a mass or inertia tensor with off-diagonal elements. These off-diagonal elements are large enough to change the mode shape of the two nearly degenerate modes from the original coordinate frame. The spring tensor is then provided with a compensating off-diagonal element, such that the mode shape is again defined in the original coordinate frame. The compensating off-diagonal element in the spring tensor is provided by a biasing voltage that softens certain elements in the spring tensor. Acceleration disturbs the compensation and the mode shape again changes from the original coordinate frame. By measuring the change in the mode shape, the acceleration is measured.

Macroscopic limit of Vlasov type equations with friction

Abstract: The purpose of this paper is to investigate the limit of some kinetic equations with a strong force. Due to friction, the solution concentrates to a monokinetic distribution so as to keep the total of force bounded and in the limit we recover a macroscopic system. This kind of asymptotics is a natural question when the mass of the particles is very small or their inertia is neglected. After that we also study the properties of the limit system and especially the uniqueness of solutions which provides the full convergence of the family of solutions to the kinetic equation.

Axisymmetric Submerged Intrusion in Stratified Fluid

Abstract: This paper presents the results of laboratory experiments conducted to study the spreading rates of axisymmetric intrusive gravity currents produced by a constant inflow into a stratified body of water. The experiments were conducted over a wide range of initial parameters. A balance of the forces that drive and retard the flow indicate that the intrusion is characterized by four spreading regimes: (1) the radial jet; (2) the radial momentum flux balanced by the inertia force; (3) the pressure (buoyancy) force balanced by the inertia force; and (4) the pressure force balanced by the interfacial drag (viscous force). The experimental results seem to confirm the derived spreading relations. The paper makes three significant contributions. It resolves theoretically and experimentally the existing conflict regarding the proper radial growth of the intrusion in the inertia-buoyancy regime. In addition, it relates the observed transition from the inertia-buoyancy regime to viscous buoyancy regime. It does so using scaling arguments to find the length and time scales for this transition. The paper also gives extensive experimental evidence for the spreading relationships in the inertia-buoyancy and viscous-buoyancy regimes, and it facilitates the determination of the corresponding experimental coefficients.

Positioning device, exposure device, and device manufacturing method

Abstract: A positioning device includes a stage which is movable along a reference surface, a stage driving mechanism for driving the stage, and an inertia imparting mechanism for reducing a reaction force produced by driving the stage. The inertia imparting mechanism has a mass body, which is movable with respect to a stage base or a structure, and a mass body driving mechanism for driving the mass body, and the stage base or structure is given inertia by driving the mass body. The inertia imparting mechanism also includes a reaction force compensation, which, by moving the mass body, reduces reaction force caused by motion of the stage, and a positioning compensation control system, which compensates for the position of the mass body. Thus, it is possible to reduce a reaction force produced by motion of the stage, and to compensate for position offset of the mass body.

An optimised short bearing theory for nonlinear dynamic analysis of turbulent journal bearings

Abstract: An approximate method for nonlinear dynamic analysis of turbulent journal bearings supporting an unbalanced rigid shaft is proposed. The method is based on two assumptions: the separation of variables for pressure and a parabolic pressure distribution in the axial direction of the bearing. To take into account inertia effects, the well-known algebraic turbulent model based on the Prandtl mixing length hypothesis is used. Using the Constantinescu's approach, the pressure equation is modified by introducing two turbulent coefficients which are depending on the local Reynolds number. The nonlinear equations of motion for the rotor-bearing system are solved by means of the Euler's scheme, and the journal centre trajectories are examined for cases with and without unbalance forces. To illustrate the validity of the present study, three cases of journal bearings are analysed. The accuracy of the minimum film thickness, the dynamic transmissibility coefficient and the peak-to-peak displacement amplitudes obtained by the proposed methodology are comparable to the more elaborate and time consuming 2-D finite difference solution, while the turbulent journal centre orbits are comparable to those obtained experimentally. It is concluded that the optimised short bearing theory shows the advantage of minimising the computation time required for nonlinear dynamic analysis of laminar and turbulent journal bearings without any significant loss of accuracy.

Dynamics of multibody vehicles and their formulation as nonlinear control systems

Abstract: We develop equations of motion for multibody vehicles that can be used for nonlinear system analysis and control design. A multibody vehicle consists of a base body that can undergo general motion in three dimensions, as well as a finite number of body interconnections that can deform relative to the base body and hence define the shape of the multibody. A Lagrangian development leads to equations of motion that are expressed in terms of the locked inertia and the mechanical connection. We show that the equations of motion can be written in terms of the base body translational and angular momentum (or equivalently the base body translational and angular velocities) and generalized coordinates for the shape. The coupling between the base body translational and rotational dynamics and the shape dynamics is made clear in this formulation. We define several fundamental categories of underactuated control problems, based on specific control actuation assumptions.

Control strategy and method for independently controlling friction element actuators for an automatic transmission

Abstract: A control strategy and method for controlling application and release of friction elements in an automatic transmission to effect gear ratio changes as one friction element is release and another friction element is applied during ratio changes. The transmission has an electronic controller and multiple solenoid regulator valves hydraulically coupled directly to pressure-operated friction elements. Powertrain variables are obtained and processed to calculate gear ratio control parameters derived from desired line pressure for a pressure control valve circuit that communicates with the friction elements. The desired gear ratio is determined for each given set of powertrain variables. Upshifts and downshifts are obtained by releasing one friction element in synchronism with an application of the other friction element, whereby a direct friction element to friction element torque transition is achieved with minimal inertia torque disturbances.

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

Abstract: 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.

Analytical Description of Meshing of Constant Pressure Angle Teeth Profiles on a Variable Radius Gear and its Applications

Abstract: This paper presents a method for determining the profile of the gear teeth on a variable radius wheel characterized by a constant pressure angle. The method can generate special gears using numerically controlled milling machines. As will be shown, the method, applied to a constant radius gear, generates an involute profile. The method is based on the integration of a differential equation describing the mesh between gears of variable radius, where the mesh point position is computed during rotation starting from the point, freely selected, where the tooth crosses the pitch line. The individual point is subsequently rotated in the opposite direction by an angle equal to the angle of rotation from the initial pitch line point, thereby generating the tooth profile. The method, applied to a wheel of variable radius, defined analytically or numerically, can compute teeth profiles on pairs of pitch lines of any shape. In particular, the motion of a slotted rotating link mechanism has been reproduced, but for the sign. Teeth profiles of other variable radius wheels have also been obtained. The results are more than satisfactory and are presented below. A numerically controlled milling machine has been programmed to actually build the anti-rotating slotted link equivalent gear. The present method, however, has much broader application, such as assigning the speed law to consequentially determine the gear form, as can be done with cams. Furthermore, a special planetary gear train makes it also possible to obtain reciprocating motion driven solely by gears. This has been built and its picture and scheme are presented in the paper. However, due to the low efficiency of the said mechanism, the best way to utilize this new technology seems to be to couple a crank and a rod to the pair of variable radius gears, as has been done at Hanover University. Some possible applications are presented. The special feature of these gears is the programmability of the shape of the pitch lines during the design phase, and thus of the velocity and acceleration profiles. In this way velocity profiles that could formerly only be obtained electro-pneumatically can be produced from purely mechanical components, with the added advantage of being able to control the level of inertia forces during the design phase.

Theoretical and experimental comparison of speed controllers for elastic two-mass-systems

Abstract: The paper presents a detailed comparison between different speed controllers for elastic two-mass systems with only a motor-side speed transducer. Each controller has been first simulated, then experimentally tested on a special mechanical test bench, featuring adjustable inertia, elasticity and load disturbance. The implementation complexity of each controller is also discussed.

Transient two-dimensional coating flow of a viscoelastic fluid film on a substrate of arbitrary shape

Abstract: The interplay between inertia and viscoelasticity, as well as the influence of gravity and substrate topography are examined in this study for the transient two-dimensional flow of a thin film. The fluid is assumed to emerge from a channel, as it is driven by a pressure gradient, which is maintained inside the channel. The substrate is assumed to be stationary. The lubrication equations are generalized for a viscoelastic fluid obeying the Oldroyd-B constitutive model. These equations are solved by expanding the flow field in Fourier modes in the vertical direction and using the Galerkin projection, combined with a time-stepping implicit scheme, and integration along the flow direction. It is found that the viscosity ratio, fluid elasticity, gravity and substrate topography can have a significant effect on transient behavior, but this effect varies significantly, depending on the level of fluid inertia. The wave and flow structures are examined for high- and low-inertia fluids. It is found that low-inertia and/or highly elastic fluids tend to accumulate near the channel exit, exhibiting a standing wave that grows with time. This behavior clearly illustrates the difficulty faced with coating viscoelastic high-viscosity fluids. In the presence of gravity, steady-state conditions are observed to be difficult to reach, even near the channel exit. The topography of the substrate has a drastic effect on the flow. A secondary wave emerges in the presence of a bump or a depression in the substrate. The wave structure is again highly dependent on the level of inertia.

Effect of Fluid Inertia on Stability of Oil Journal Bearings

Abstract: In the analysis of hydrodynamic journal bearings the effect of fluid inertia is generally neglected in view of its negligible contribution compared to viscous forces. However, the fluid inertia effect is to he taken in the analysis when modified Reynolds number is around one. Though there are a few attempts to analyse steady-state and dynamic characteristics of finite journal bearings, stability of the journal under the effect of fluid inertia is yet to he investigated. An attempt has been made to evaluate the mass parameter (a measure of stability) besides finding out the steady-state characteristics of finite journal bearings considering the effects of fluid inertia. The analysis is carried out for modified Reynolds number ∼O(l.), which is assumed to be laminar. A nonlinear time transient analysis is carried out for the stability analysis.