Linear Theoretical Model Research Articles

Modeling of Computer-Controlled AC Servo Feed System

This paper will be devoted to build a mathematical model of this kind based on the computer-controlled AC servo feed system of a common XY worktable. First, a practical AC servo worktable system is analyzed and its linear theoretical mathematical model is given. Second, the parameter in this model is identified in terms of the actual measured output data and reference signal by using an ARX model by using RLS identification method. Then, by using servo “simulation” techniques, a very accurate model of the servo drive can be constructed. Based on this model, it is possible to observe the effect on performance by changing the factors such as backlash, friction, servo-loop gains. Hence, a deep understanding of dynamics of the computer-controlled AC servo feed system of a common XY worktable is obtained. It is expected that this paper will lay reliable foundation for the further work—friction compensation, so that the precision of the system will be improved in the end.

Theoretical development of a graphical analysis technique to optimize the particle size distribution of pigments in paints and coatings

The new analytical expression introduced in this study shows that a plot of the accumulated volume fraction of pigment particles vs. the square root of particle size should be a straight line for the theoretically preferred particle size distribution. This linear theoretical model was also found to be consistent with the experimentally developed linear model proposed by Kaeuffer. However, Kaeuffer proposed that his straight line went through the origin, but the analytical model developed in this paper has shown that this intercept is not zero. Thus, Kaeuffer’s experimental model is only partially correct.

Lateral Stability Simulation of a Rail Truck on Roller Rig.

The development of experimental facilities for rail vehicle testing is being complemented by analytic studies. The purpose of this effort has been to gain insight into the dynamics of rail vehicles in order to guide development of the Roller Rigs and to establish an analytic framework for the design and interpretation of tests to be conducted on Roller Rigs. The work described here represents initial efforts towards meeting these objectives. Generic linear models were developed of a freight car (with a characteristic North American three-piece truck) on tangent track. The models were developed using the generalized multi body dynamics software MEDYNA. Predictions were made of the theoretical linear model hunting (lateral stability) characteristics of the freight car, i. e., the critical speeds and frequencies, for five different configurations: (a) freight car on track, (b) the freight car's front truck on the roller stand and its rear truck on track, (c) freight car on the roller rig, (d) a single truck on track, and (e) single truck on the roller stand. These were compared with the Association of American Railroads' field test data for an 80-ton hopper car equipped with A-3 ride control trucks. Agreement was reached among all the analytical models, with all models indicating a range of hunting speeds of 2% from the highest to lowest. The largest discrepancy, approximately 6%, was indicated between the models and the field test data. Parametric study results using linear model of freight truck on the roller rig show that (a) increasing roller radius increases critical speed (b) increasing the wheel initial cone angle will decrease the hunting speed (c) increasing the roller cant increases hunting speed (d) decrowning of the wheelset on the rollers will not effect the hunting speed but induces longitudinal destabilizing horizontal forces at the contact and (e) lozenging of wheelset on the rollers induces a yaw moment and the hunting speed decreases with increasing wheelset yaw angle.

Lateral stability analysis of a railway truck on roller rig

The development of experimental facilities for rail vehicle testing is being complemented by analytic studies. The purpose of this effort has been to gain insight into the dynamics of rail vehicles in order to guide development of the roller rigs and to establish an analytic framework for the design and interpretation of tests to be conducted on roller rigs. The work described here represents initial efforts towards meeting these objectives. Generic linear models were developed for a freight car (with a characteristic North American three-piece truck) on tangent track. The models were developed using the generalized multi body dynamics software MEDYNA. Predictions were made of the theoretical linear model hunting (lateral stability) characteristics of the freight car, i.e., the critical speeds and frequencies, for five different configurations: (a) freight car on track, (b) the freight car’s front truck on the roller stand and its rear truck on track, (c) freight car on the roller rig, (d) a single truck on track, and (e) single truck on the roller stand. These were compared with the Association of American Railroads (AAR) field test data for an 80-t hopper car equipped with A-3 ride control trucks. Agreement was reached among all the analytical models, with all models indicating a range of hunting speeds of 2% from the highest to lowest. The largest discrepancy, approximately 6%, was indicated between the models and the field test data. Parametric study results using linear model of freight truck on the roller rig show that: (a) increasing roller radius increases critical speed, (b) increasing the wheel initial cone angle will decrease the hunting speed, (c) increasing the roller cant increases hunting speed, (d) decrowning of the wheelset on the rollers will not effect the hunting speed but induces longitudinal destabilizing horizontal forces at the contact, and (e) lozenging of wheelset on the rollers induces a yaw moment and the hunting speed decreases with increasing wheelset yaw angle.

Dynamics of electron-plasma vortex in background vorticity distribution.

Dynamics of a point vortex in interaction with a broad profile of background vorticity is studied experimentally by using an electron plasma. The observed motion of the vortex compares favorably with a recently proposed theoretical model [D. A. Schecter and D. H. E. Dubin, Phys. Rev. Lett. 83, 2191 (1999)]. Perturbations in the background distribution in the wake of the spiral orbit of the vortex amount to several tens of percent and are considered to be a major reason for deviations of the observation from the linear theoretical model.

GRAVITY EFFECTS ON THE COUPLED FREQUENCIES OF A 2D FLUID–STRUCTURE PROBLEM WITH A FREE SURFACE

This paper discusses an experimental study of the coupled frequencies of a flexible structure partially immersed in a fluid in a finite container, in two dimensions, with non-negligible gravity effects. The results are compared with those obtained using a theoretical linear model including surface tension and meniscus length. The good agreement obtained validates this theoretical model. Curves are then presented for the coupled frequencies vs the fluid level in this container for various values of the gravity.

LATERAL STABILITY ANALYSIS OF A RAILWAY TRUCK ON ROLLER RIG

Generic linear models were developed of a freight car (with a characteristic North American three-piece truck) on tangent track. The models were developed using the generalized multi-body dynamics software MEDYNA. Predictions were made of the theoretical linear model hunting (lateral stability) characteristics of the freight car, i.e., the critical speeds and frequencies, for five different configurations: (a) freight car on track, (b) the freight car’s front truck on the roller stand and its rear truck on track, (c) freight car on the roller rig, (d) a single truck on track and (e) single truck on the roller stand. These were compared with the Association of American Railroads’ field test data for an 80-ton hopper car equipped with A-3 ride control trucks. Agreement was reached among all the analytical models, with all models indicating a range of hunting speeds of 2% from the highest to lowest. The largest discrepancy, approximately 8%, was indicated between the models and the field test data.

MODELLING AND SIMULATION OF THE HUNTING OF A THREE-PIECE RAILWAY TRUCK ON NRC CURVED TRACK SIMULATOR

SUMMARY Generic linear models were developed of a freight car (with a characteristic North American three-piece truck) on tangent track and on NRC's Curved Track Simulator (CTS). The models were developed using the generalized multi body dynamics software MEDYNA. Predictions were made of the theoretical linear model hunting (lateral stability) characteristics of the freight car, i.e., the critical speeds and frequencies, for five different configurations: (a) freight car on track, (b) the freight car's front truck on the CTS and its rear truck on track, (c) freight car on the CTS, (d) a single truck on track, and (e) single truck on the CTS. These were compared with the Association of American Railroads' field test data for an 80-ton hopper car equipped with A-3 ride control trucks. Good agreement was achieved among all the analytical models, with all the models indicating a range of hunting speeds of 2% from the highest to lowest. The largest discrepancy, approximately 6%, was indicated between the model...

A minimal cost function method for optimizing the age‐Depth relation of deep‐sea sediment cores

The question of an optimal age‐depth relation for deep‐sea sediment cores has been raised frequently. The data from such cores (e.g., δ18O values) are used to test the astronomical theory of ice ages as established by Milankovitch in 1938. In this work, we use a minimal cost function approach to find simultaneously an optimal age‐depth relation and a linear model that optimally links solar insolation or other model input with global ice volume. Thus a general tool for the calibration of deep‐sea cores to arbitrary tuning targets is presented. In this inverse modeling type approach, an objective function is minimized that penalizes: (1) the deviation of the data from the theoretical linear model (whose transfer function can be computed analytically for a given age‐depth relation) and (2) the violation of a set of plausible assumptions about the model, the data and the obtained correction of a first guess age‐depth function. These assumptions have been suggested before but are now quantified and incorporated explicitly into the objective function as penalty terms. We formulate an optimization problem that is solved numerically by conjugate gradient type methods. Using this direct approach, we obtain high coherences in the Milankovitch frequency bands (over 90%). Not only the data time series but also the the derived correction to a first guess linear age‐depth function (and therefore the sedimentation rate) itself contains significant energy in a broad frequency band around 100 kyr. The use of a sedimentation rate which varies continuously on ice age time scales results in a shift of energy from 100 kyr in the original data spectrum to 41, 23, and 19 kyr in the spectrum of the corrected data. However, a large proportion of the data variance remains unexplained, particularly in the 100 kyr frequency band, where there is no significant input by orbital forcing. The presented method is applied to a real sediment core and to the SPECMAP stack, and results are compared with those obtained in earlier investigations.

A Linear Theory of Vibrations Caused by Ball Bearings With Form Errors Operating at Moderate Speed

A linear theoretical model is presented for the vibrations of a shaft bearing system caused by ball bearing geometrical imperfections. It is valid for low and medium speeds where ball centrifugal forces can be neglected. The excitation forces from each bearing are calculated and can serve as input to suitable rotor dynamics programs. Imperfections covered are radial and axial waviness of outer and inner rings, ball waviness and diameter distribution, nonuniform cage pocket distribution.

Excitation of large-amplitude ion-wave wake fields.

Plasma wake fields in the ion-wave regime have been excited by injecting ion bunches with a variety of shapes. An excited-wave amplitude (\ensuremath{\delta}n/${\mathit{n}}_{0}$) of up to 17% has been observed for a bunch falloff time less than the wake-field period. The large-amplitude wake wave damps out, along with oscillations of the wave envelope. A simple linear theoretical model is developed, which can explain most of the observed phenomena, except for the large-amplitude oscillations.

Spurious Gratings Due to Internal Reflections in Dichromated Gelatin

Abstract Transmission holograms in dichromated gelatin are studied under conditions when a number of spurious gratings (both transmission and reflection types) are also present due to boundary reflections at recording. It is shown that the experimental results, in the form of transmitted power against incident angle measured on the developed hologram, agree well with the predictions of a simple, linear theoretical model based on coupled wave theory.

AN INVESTIGATION INTO THE INTERACTION BETWEEN VEHICLE RIDE AND TILT SYSTEMS

SUMMARY This paper describes the development of a linear theoretical model of a tilting vehicle to study the interaction between the tilt system and the passive ride of the vehicle on straight track. Predictions made with the model show transmission of significant roll activity through the tilt system at the suspension frequencies for certain combinations of speed and conicity. The predictions are compared with results from a series of tests on a tilting vehicle. The principal interactions between tilt and ride demonstrated by the model compare qualitatively with the test results. Quantitatively, there is scope for improvement because deficiencies in linear modelling which exist for all vehicles are compounded by the complexity of the mechanical design of a tilting train. The method can be extended to predict system response at curve entry and has considerable potential as a tool for the designer of tilting trains.

Fluorescence inner filtering in double-pass cell configurations. Part 2. Validity of assumptions for primary inner filtering diagnosis

In Part 1 relationships were derived for primary inner filtering in double-pass cell configurations leading to an equation that is useful for diagnosing primary inner filtering. Unfortunately, the non-linearity of the experimental curve represented a significant departure from the linear theoretical model although some artifacts associated with the instrumentation predicted a minor departure of the experiment from linearity. Other assumptions such as beam collimation and fluorescence emission radiating from a point source centred in the cuvette were used, although invalid for most spectrofluorimeters. In this paper these two assumptions are evaluated, bringing the experimental working curves into closer agreement with the theoretical relationship.

The Effect of a Normal Shock on the Aeroelastic Stability of a Panel

The effect of a standing shock wave on the static and dynamic aeroelastic stability of a flexible panel is investigated using a linear structural and aerodynamic theoretical model. It is found that the shock is generally stabilizing. The lowest critical dynamic pressures are associated with shock positions downstream from the panel, where the panel is uninfluenced by the shock.

Volume transport of the western boundary current penetrating into a marginal sea

The amount of penetration of a western boundary current into a marginal sea which is connected to an open ocean by two narrow straits is estimated from a linear, steady and barotropic theoretical model. In this model the western boundary current in the open ocean is driven by a wind stress imposed at the sea surface. The inflow of the water of the open ocean into the marginal sea is caused by the pressure difference between two straits produced by the wind-driven circulation in the open ocean.

Optimization of Thick Film Resistors for Low Drift

In order to minimize drift in a thick film resistor both printing and trimming parameters have to be optimized carefully.With the aid of a linear theoretical model it is shown how the resistance drift in the bulk transition zone and terminals of the resistor can be calculated for both trimmed and untrimmed resistors.The theoretical results are used for optimization of laser trimmed high ohmic resistors. The experimental results are in good agreement with the theoretical predictions and confirm that thick film resistors can be optimized for low drift.

A Multivariable Autoregressive Model of the Dynamics of a Boiling Water Reactor

An autoregressive (AR) model with pseudo-random binary sequence (PRBS) test signals was applied to the dynamics of the Japan Power Demonstration Reactor, a boiling water reactor (BWR). The decision of the order of the AR model was based on the Akaike criterion. Multi-input test signals of the PRBS were applied to the steam-flow control valve and the forced circulation pump speed control terminal. Seventeen variables including the instrumented fuel assemblies were observed. The AR model identification facilitated building the BWR dynamics model as a multivariable system. The experiment indicated that the BWR dynamics with rather intensive nonwhite noise interference was effectively represented by the AR model, which was compared with a linear theoretical dynamics model. The results suggested that the identified AR model plays an important role in verifying, modifying, and improving the theeoretical dynamics model.

Excitation of hide waves in the core due to transient-spatially periodic stress in the lower mantle

Forced hydromagnetic oscillations in the outer core due to stress at its top are studied by means of a simple linear theoretical model originally proposed byHide [1] for the free oscillation studies. Both the magnetic and the inertial modes are excited. The expressions for the velocity, magnetic and vorticity fields are presented for a variety of stresses. They depend upon the wave number and frequency. In a numerical example wherein the stress varies periodically both in the space and the time, the amplitude of the induced magnetic field is found to be significant for reasonable values of various parameters.

Theoretical analysis of force distribution on lower partial dentures with symmetric saddles

It is difficult to make direct measurements of the displacement of a partial denture as a function of the magnitude and direction of a force applied to the occulusive surface of the denture teeth during chewing. An indirect approach is possible, using a theoretical model in conjunction with some particular experimental measurements that are easier to make. The purpose of this paper is to present a theoretical linear model. The origin of the coordinate system is chosen at the tissue level under the center of the lower first molar. We first compute the total depth to which an arbitrary point on the ridge crest line will go when the denture is depressed into the ridge tissue during mastication. Using the approximation of linear depth force relationship, we find: A X=B where A is the shape and size coefficient matrix, B is the mastication-force column matrix, and X is the unknown column matrix which includes both the movement of reference points and the reactive force.