bluuebunny/crossref_metadata_2025 huggingface dataset:
Investigation of Optimal Control With a Minimum-Fuel Consumption Criterion for a Fourth-Order Plant With Two Control Inputs; Synthesis of an Efficient Suboptimal Control
Authors: Craig A. J. , Flu¨gge-Lotz I.
Published: November 2011

Application of Pontryagin’s optimal principle to control system problems eventually requires that a two-point boundary-value problem be solved. For plants whose equations of motion are greater than second order this represents a formidable barrier in realizing a practical feedback control. When the criterion for optimization is minimum-fuel consumption, choice of time for solution may be used as a free parameter, and this plus consideration of the efficiency of application of control leads to an approximate method which avoids this difficulty. A heuristic analysis of the geometry of state-space trajectories, using true optimal solutions as a guide, provides laws for constructing a feedback control from the state variables. It further provides a knowledge of the bounds of performance of the mechanized suboptimal control and an estimate on the performance of a minimum-time control for comparison purposes. As an example, the method is applied to the problem of minimum-fuel attitude control of an earth-orbiting satellite, a fourth-order plant with two controls.
Some Design Techniques for Fluid-Jet Amplifiers
Authors: Wright C. P.
Published: November 2011

The operation of the fluid-jet amplifier is described briefly. A performance criterion is developed for the amplifiers, and design techniques are presented which constrain the amplifier to exhibit the decision function. The techniques involve the superposition of a bias on the amplifier which alters its switching characteristics. In addition, a stability criterion for amplifier operation is developed and its uses are suggested. Some effects of internal geometry variations are also discussed.
On a Problem of Letov in Optimal Control
Authors: Johnson C. D. , Wonham W. M.
Published: November 2011

In a series of papers [1, 2], A. M. Letov discussed an optimal regulator problem for a linear plant with bounded control variable and quadratic performance index. This problem was also discussed by Chang [3]. Krasovskii and Letov observed later [4] that the solution proposed in [1, 2, and 3] may be correct only for special choices of the initial value of the state vector. In the present note, further aspects of the solution in the general case are described and three examples are given. The possible existence of a regime of unsaturated-nonlinear optimal control is demonstrated. The presence of this regime in the optimal control law was apparently overlooked in [1–4].
Bending of Thick Steel Plates
Authors: Junker A. T.
Published: November 2011

The surface strains on an initially flat plate bent to a cylindrical shape are considered and compared to the biaxial rupture strain limit of the material. A procedure for predicting the bending limit of a plate is developed which is based on the Ludwik law. An example is presented to illustrate the case of a typical severe bending operation in which surface strains approached the ductility without fracture of the formed plate.
The Static and Dynamic Characteristics of the Spiral-Grooved Thrust Bearing
Authors: Malanoski S. B. , Pan C. H. T.
Published: November 2011

A generalized analysis for spiral-grooved thrust bearings is presented. The effects of local radius are considered. For the same grooving geometry and the same inside-to-outside radius ratio, the inflow design is shown to be superior in both stiffness and load capacity. The analysis also treats a relative, transverse, oscillatory motion of the bearing surfaces. Both the magnitude and phase angle (in the temporal sense) of the bearing reaction are dependent on the frequency of the motion. The results for the oscillating motion reveal the possibility of a self-excited, rotor-bearing instability. The criterion for determining the onset of this type of instability is given.
On the Behavior of Gas-Lubricated Journal Bearings Subjected to Sinusoidally Time-Varying Loads
Authors: Ausman J. S.
Published: November 2011

Linearized steady-state time-dependent solutions to the equations of journal motion are obtained for sinusoidally time-varying radial loads by utilizing the “linearized ph” technique to approximate lubricant pressure forces. An exemplary check for vibration at half-rotor frequency shows that the nonlinear terms can be neglected provided the total eccentricity ratio (static plus dynamic) remains less than one half. A typical journal-bearing frequency response exhibits two distinct types of resonances: One at half-rotor frequency and another at a frequency given by K/M, where K is the effective spring constant due to the bulk modulus of the gas lubricant and M is the mass of the supported rotor. As the static eccentricity ratio ∈0 increases, the amplitude of the half-rotor frequency resonance decreases drastically, but the amplitude of the K/M resonance increases slightly. Rotating load response can be synthesized by superimposing the responses to two 90 deg out-of-phase radial loads acting along perpendicular axes. The resulting response is a nearly circular ellipse centered about the static equilibrium position.
Design and Performance of Gas-Pressurized, Spherical, Space-Simulator Bearings
Authors: Wilcock D. F.
Published: November 2011

Space-simulator bearings of the externally pressurized gas-lubricated type must meet a number of unusually stringent requirements. Of primary importance is that they contribute as nearly as possible zero error torque to the supported simulator structure, and that changes in this torque as the structure is rotated as desired about all three axes be extremely small. The bearing must be stable and free of vibration under all conditions; and in the more sophisticated simulators, the bearing must sustain lateral as well as vertical loads with close control of film thickness. Low-error torque requires first of all that the rotatable sphere be both geometrically perfect and flawless of surface. Errors in the bearing causing roll and pitch torques can be balanced out by the table balance weights; but azimuth torques cannot be counterbalanced. They are minimized by appropriate bearing design which places the gas-flow lines in planes passing through the azimuth axis. Bearing-design parameters and equations are established. A detailed computer analysis explains why these bearings cannot be operated below a certain minimum film thickness. Error torques resulting from flaws or scratches in the bearing and sphere surfaces are analyzed and found to increase with film thickness. Bearing-error torque is found to increase as the square of the load.
Theory of Externally Pressurized Circular Thrust Porous Gas Bearing
Authors: Mori H. , Yabe H. , Ono T.
Published: November 2011

The externally pressurized circular thrust gas bearing with porous bearing surface is analysed here theoretically. The authors use “permeability coefficient” which identifies the characteristic of porous media, and introduce the concepts of the “equivalent clearance” and the “effective restricting thickness” of the porous layer so that the flow through the porous material can be analyzed in both axial and radial directions, and the flow in the porous material and the bearing clearance may be considered as two parallel flows connected with each other. The analysis coincided qualitatively as well as quantitatively with the results of the experiments concerning the pressure distribution and the load capacity.
A Numerical Solution for the Pressure, Temperature, and Film Thickness Between Two Infinitely Long, Lubricated Rolling and Sliding Cylinders, Under Heavy Loads
Authors: Cheng H. S. , Sternlicht B.
Published: November 2011

A nummerical solution to the coupled Reynolds, elasticity, and energy equations for the pressure, temperature, and film thickness between two heavily loaded rolling and sliding cylinders is obtained. The analysis of the energy equation is based on a mean viscosity across the film. Results for a thermal case with a slip ratio of 0.25 as well as an isothermal solution are presented. Pressure peak is found near the exit of the film for cases with or without thermal effects and the influence of the temperature on the film thickness is moderate.
The Action of Neutral Organic Phosphates as EP Additives
Authors: Barcroft F. T. , Daniel S. G.
Published: November 2011

A radiochemical analysis has been made of the EP film formed on the surfaces of the tappets of an engine lubricated with an oil containing triphenyl phosphate, labeled with phosphorus –32, as the EP additive. The results do not support the widely held view that phosphate esters owe their effectiveness as EP additives to the formation of phosphide eutectics of low melting point on metal surfaces. The results indicate the presence of metal phosphates and metal organophosphates formed from acid-phosphate intermediates derived from the ester. These findings, together with the results of subsequent rig tests, suggest that the effectiveness of neutral organic phosphates as EP additives depends on the ease with which they hydrolyze on the metal surface to form acid phosphates; the more readily the ester hydrolyzes the better its performance.
Resonance in Liquid Rocket Engine Systems
Authors: Fashbaugh R. H. , Streeter V. L.
Published: November 2011

A transient flow analysis of a longitudinal vibration in a liquid rocket engine propellent feed system and its supporting structural framework is described, together with supporting experimental tests. Nonlinear friction losses are used in the partial differential equations of continuity and momentum describing the unsteady flow. These equations are solved by the methods of characteristics and placed in form suitable for digital computation. The turbopump steady-state characteristic curves are used to find the transient pressure rise across the pump, and the effects of pump inlet cavitation are estimated from experimental data.
Determination of ASME Nozzle Flow Coefficients by Thrust Measurement
Authors: Reimer Robert M.
Published: November 2011

This paper describes the recently developed thrust-measurement technique, a quasi-primary method, that is capable of calibrating very large ASME nozzles. The technique is an application of Newton’s law, force equals mass-flow rate times velocity. Application of boundary-layer theory allows the flow coefficient to be calculated from the thrust force, area, and pressure measurements. Test data indicate that the flow coefficient of ASME nozzles flowing compressible gas at high pressure ratio increases with throat diameter, independent of Reynolds number, and is about 1/2 percent lower than the coefficient for incompressible fluid at the same Reynolds number. This thrust-measurement technique has been used successfully to prove the thrust-measurement capability of many aircraft-jet nozzle test facilities.
Elastic Shell-Theory Formulation for Bourdon Tubes
Authors: Dressler Robert
Published: November 2011

The stress-displacement problem is considered for a typical bourdon tube in equilibrium deflection resulting from internal fluid pressure. In contrast with many analyses using approximations and simplifications, here the exact (linear) elastic-shell theory is employed, applied to a tube having elliptical cross section and with central line forming a circular arc. Differential-geometry quantities for the surface are derived as required for shell theory, and the explicit form is obtained for the partial differential equations, referenced to the lines of principal curvature as orthogonal curvilinear coordinates. Equations are presented for the Love-type shell theory and for a Donnell-type theory, both including the interacting bending and membrane effects. The rigid plug at the free end of a bourdon tube creates some complexity in the boundary conditions: These must be considered in-the-large rather than at each boundary point, to obtain the correct number of imposed relations for a determinate problem. The original problem is finally reduced to a specific computational problem for five partial differential equations of order eight, plus certain integral boundary relations, in a rectangular domain.
Contact Pressures and Stresses in One Theoretically Investigated Case
Authors: Petrusevich A. I.
Published: November 2011

The investigated case is: Two rotating steel cylinders, infinitely long and with effective radius of curvature of 5 cm, are loaded to Hertzian pressure of approximately 5000 kg/cm2 and are lubricated by an oil. The composite effect of peripheral speed and viscosity (under a given surface temperature) is necessary to build up a lubricating film with a thickness of 1 micron. The solution is approximate and found by the use of elastohydrodynamic theory.
Plane-Contact Problem of Thermoelasticity During Quasi-Stationary Heat Generation on the Contact Surfaces
Authors: Korovchinski M. V.
Published: November 2011

When determining the surface temperature on the contact of two rubbing bodies employing the widely used method offered by Block, it is assumed that the distribution of pressure in the contact area remains similar to the distribution when the heat generation caused by friction is absent. But actually, if there is even a slightly noticeable heat generation on the surfaces of the contact, a local bulging appears near the contact area owing to the heat expansion of the rubbing bodies. This bulging changes the curve and consequently the law of distribution of pressure as compared to that of Hertz. The latter in its turn leads to alteration of maximum temperatures as compared to the universally adopted values. This paper deals with the composition and then with the solution of the basic integral-differential singular equation for distribution of pressures across the contact strip for the case of two contacting cylinders with parallel axes; the distribution of surface temperature is then found.
Hydromagnetic Squeeze Films Between Two Conducting Surfaces
Authors: Shukla J. B. , Prasad R.
Published: November 2011

This paper gives an analytical investigation of the hydromagnetic theory for squeeze films between two conducting surfaces. It is shown that increase in load capacity, pressure, and time of approach are possible by increasing either the strength of the magnetic field, or conductivities of the surfaces, or both.
Uranium-Molybdenum Alloy for Use in a Prompt-Burst Reactor
Authors: Rienecker F. , Moran W. H.
Published: November 2011

A large prompt-burst nuclear reactor, “Super Kukla,” required a core of material that would withstand unusually high stress levels resulting from rapid thermal expansion and inertia loads. An experimental investigation was undertaken to determine the properties of cast uranium—10 wt percent molybdenum alloy under static and dynamic conditions of loading at various temperatures for application in this reactor. Techniques were developed to cast, inspect by radiographic and ultrasonic means, machine, and nickel plate the material. Castings are in the form of rings, 30 in. OD, 18 in. ID, and 2 in. thick. Sound material with carbon content of less than 250 ppm was found to have a static yield strength of approximately 130,000 psi, ultimate strength of 133,000 psi, and elongation of 10 percent at room temperature. Sustained static loads of more than 40,000 psi in a normal atmosphere were found to induce a brittle fracture attributed to stress corrosion. Test specimens subjected to strain rates on the order of 20 in/in/sec withstood stresses of 200,000 psi in the gage region, but usually failed in the threaded ends.
An Approximate Analysis of Deflections of Beams in Creep Bending
Authors: Meck H. R.
Published: November 2011

A method is developed for estimating deflections in beams subjected to creep bending. Many structures which require lengthy calculations when solved by conventional methods can be analyzed easily by the present procedure. The method is illustrated by a series of examples. Both statically determinate and indeterminate cases are considered.
Computation of the Critical Flow Function, Pressure Ratio, and Temperature Ratio for Real Air
Authors: Reimer Robert M.
Published: November 2011

A method of computing the critical flow function, critical pressure ratio, and critical temperature ratio is presented. Use is made of the NBS Circular 564 tabulated data of the speed of sound, enthalpy, and compressibility. Computations are made for dry real air at stagnation temperature from 60 to 100 F and stagnation pressure from zero to 300 psia. The change in the flow function and ratios is 0.9, 0.5, and 0.4 percent, respectively, over this range. Calculations are also performed at elevated pressure and temperature.
Theory for Supercavitating Flow Through an Arbitrary Form Hydrofoil
Authors: O¯ba R.
Published: November 2011

An accurate theory which included the following two methods was developed concerning the flow through an arbitrary form supercavitating hydrofoil: (i) A method by which to obtain the hydrofoil form for a given pressure distribution; (ii) a method by which to estimate hydrofoil characteristics. The accuracy of the previously reported linearized solution was checked on, and then a very simple effective correcting method for the linearized solution was found out.
Geometry Effects on the Threshold of Half-Frequency Whirl in Self-Acting, Gas-Lubricated Journal Bearings
Authors: Sternlicht B. , Winn L. W.
Published: November 2011

It has been shown that half-frequency whirl is influenced by orifice location, number of grooves, groove location, and so on. This paper presents test results which show the effect of geometry on the threshold of half-frequency whirl. The following bearing configurations were tested: (a) Plain journal bearings with one orifice centrally located; (b) grooved journal bearings with two axial grooves; (c) grooved journal bearings with three axial grooves; (d) grooved journal bearings with three axial grooves and six orifices. In addition, load-carrying capacity and attitude angle for the plain cylindrical and the two and three axial-groove bearings with two groove positions are given.
Some Applications of the Maximum Principle to Second-Order Systems, Subject to Input Saturation, Minimizing Error, and Effort
Authors: Boyadjieff G. , Eggleston D. , Jacques M. , Sutabutra H. , Takahashi Y.
Published: November 2011

The optimal controls for various types of performance criteria are investigated for second-order systems by means of the Pontryagin’s Maximum Principle. Optimal control solutions for several examples are shown. The results presented show widely different modes of control depending upon the performance criteria, and also indicate a possibility of closed loop control. The methods used in the various solutions may be extended to other performance criteria and systems.
On Adaptive Optimal Control of Nonlinear Processes
Authors: Pearson A. E.
Published: November 2011

The paper concerns an approach to adaptive optimal control of nonlinear dynamic systems which has been introduced by Kulikowski. In this approach, the required identification is carried out at each stage of constructing a sequence of inputs (xn(t)), tε(0, T) converging to a relative extremum of a given performance functional. The major contributions of this paper relate to the identification problem and its incorporation into the optimal control formulation.
Minimum Fuel Control of a Second-Order Linear Process With a Constraint on Time-to-Run
Authors: Ladd H. O. , Friedland Bernard
Published: November 2011

The optimal control as a function of the instantaneous state, i.e., the optimal “feedback” or “closed-loop” control, is derived for the controlled second-order linear process with constant coefficients x¨+2bx˙+c2x=u for so-called minimum-fuel or minimum-effort operation (i.e., such that the time integral of the magnitude of the control u is minimized), subject to an amplitude limitation on the control |u| ⩽ L. The objective is to force the phase state from an arbitrary instantaneous value (x, x˙) to the origin within an arbitrarily prescribed time-to-run T. The solution is obtained for the nonoscillatory cases (b2 ⩾ c2 ⩾ 0) when L is finite, and for arbitrary real b and c when L is infinite; i.e., when the control is not amplitude-limited. The form of the optimal control is shown to be “bang-off-bang” with the most general initial conditions; i.e., during successive time intervals, u is constant at one limit, identically zero, and constant at the limit of opposite polarity. Explicit expressions for the switching surfaces in state space (T, x, x˙) at which u changes value and, hence, of the optimal feedback control u (T, x, x˙), are given, both with and without amplitude limitation. Without such (L = ∞) the optimal control is impulsive and the areas of the impulses in terms of the current state are obtained by a limiting procedure.
Stability Study of PWM Feedback Systems
Authors: Jury E. I. , Nishimura T.
Published: November 2011

A fundamental equation which yields the limit-cycle feature of PWM feedback system is derived in this paper. The application of this equation to obtain the response of the autonomous as well as the forced PWM system is indicated. The application of this fundamental equation to other types of nonlinear sampled-data feedback systems is also demonstrated. The maximum mode of the limit cycles that can exist in relay-mode oscillations of PWM systems as well as the limitations on the maximum period is obtained in this paper. Based on the foregoing derivations, the sufficient conditions for eliminating all saturated oscillations is derived. The experimental study performed on the digital computer confirms the theoretical results. Stability curves for certain PWM systems are being calculated which will aid considerably in this design. The basic advantage of PWM controllers on relay sampled-data systems with regard to sensitivity and stability is well pointed out in this paper as well as a few examples illustrating the application of the fundamental equations derived.
A Counterbalance System for Dynamic Testing of Equipment Designed to Operate in a Zero-G Field
Authors: Nicklas J. C.
Published: November 2011

The development and design considerations of a counterbalance system utilizing a servomechanism are given. The purpose of the counterbalance system is to allow dynamic testing of equipment to be used in a zero-g field. The problem of cancellation of gravitational torques and obtaining valid test data is discussed. Various techniques of counterbalancing are investigated. The method having the most flexibility uses a servo-mechanism and an energy-storage device. For this system a linear torsion spring is attached to the device being counterbalanced and is used for the energy-storage element. A strain gage gives a voltage indicating the counterbalance torque being applied by this spring. The reference voltage is proportional to the counterbalance torque required and comes from a resolver. The difference between these two signals controls the position of the other end of the torsion spring. With this mechanization it is shown that the requirements on the performance of the servomechanism are not severe. It is concluded that the technique using an energy-storage device and a servomechanism offers advantages which other techniques do not. The possibility of using other mechanizations of this counterbalancing technique is discussed.
Magnetohydrodynamic Squeeze Films
Authors: Kuzma D. C.
Published: November 2011

An analysis of hydrodynamic squeeze films is presented for the case of an electrically conducting fluid in the presence of a magnetic field. Circular plates and infinitely long rectangular plates are considered with a uniformly applied magnetic field. The relationships between fluid-film thickness and time are determined analytically and compared with the ordinary hydrostatic squeeze films. It is shown that the application of a magnetic field improves the squeeze-film action.
The Critical Flow Function for Superheated Steam
Authors: Murdock J. W. , Bauman J. M.
Published: November 2011

Computations are made of the theoretical critical flow rate of superheated steam through nozzles or other passages. Flow maximization was used in determining the critical function φ=GT11/2/p1. Tabulations of the critical flow function are given for the “superheated vapor” region defined by Keenan and Keyes “Steam Tables” with a pressure limitation of 5000 psia. Two approaches are presented to relate the critical flow function to an ideal state. In the first approach the temperature of the throttled vapor, from inlet conditions, to a very low pressure (p = 0.08854 psia) was used. The second approach utilized the equivalent ideal-gas stagnation temperature that steam would have if its compressibility factor was unity. A dimensionless correlation on reduced coordinates is presented for the second approach, which permits the correlation of steam data to hydrocarbons or other nonideal gases the compressibility factors of which are available as functions of reduced coordinates. A practical method for calculating theoretical critical flow is presented utilizing the properties of steam as taken directly from the Keenan and Keyes “Steam Tables.”
Some Comparisons Between Compressible and Incompressible Treatments of Compressible Fluids
Authors: Benedict R. P.
Published: November 2011

In this paper we are concerned with the degree of approximation made when various common parameters involved in an isentropic, compressible fluid flow are evaluated from incompressible relations. First, compressible and incompressible solutions are derived and presented graphically. Then, ratios between these compressible and incompressible treatments are formed which define various expansion factors; these are tabulated and presented graphically. Several numerical examples illustrate the use of the tables and graphs.
Flow Nozzles With Zero Beta Ratio
Authors: Leutheusser Hans J.
Published: November 2011

An analytical expression for the discharge coefficient of ASME long-radius flow nozzles with zero beta ratio is presented. The latter condition corresponds to the installation of a metering nozzle at the outlet from a very large supply reservoir. The prediction of the theoretical equation is compared with experimentally determined discharge coefficients for nozzles of this type. Reference is made to analytical work in this field by other investigators and conclusions are drawn as to the degree of analytical sophistication required in order to obtain satisfactory agreement between analytical and experimental data.
Two-Phase Flow in Capillary Tubes
Authors: Suo Mikio , Griffith Peter
Published: November 2011

The adiabatic flow of two phases, gas and liquid, has been studied in horizontal tubes of capillary diameter. The flow has been studied primarily in the regime where the gas flows as long bubbles separated from the wall of the tube by a liquid film and from each other by slugs of liquid. In this regime the density and the thickness of the liquid film around a bubble have been correlated. The conditions under which the long bubble flow can exist and under which the correlations are valid have been determined.
The Nature of Self-Excitation in the Flow-Induced Vibration of Flat Plates
Authors: Eagleson P. S. , Noutsopoulos G. K. , Daily J. W.
Published: November 2011

Flow-induced vibrations of flat plates are studied in water. An equation of motion of the plate-spring system is formulated incorporating the hydrodynamic loads given by the linearized potential theory, and the unknown, vortex-induced, forcing moments. Considerations of bluff-body wake dynamics show the coefficient of this forcing moment to be a function of the steady-body Strouhal number, the chord-to-thickness ratio, and a self-excitation parameter which contains the transverse body motion. This function is evaluated for plates with different trailing edges using experimental measurements of vibrational amplitude and frequency, and the nature of its dependence on vibration is shown to be equivalent to a negative damping. The poles of the amplitude-response relation are shown to predict the bounds of the zone in which large vibrational (“singing”) motion occurs. Criteria are offered for the design of systems to avoid these self-excited vibrations.
Inverse Methods in the Linearized Theory of Fully Cavitating Hydrofoils
Authors: Parkin B. R. , Grote R. S.
Published: November 2011

Theoretical and numerical procedures are given for the design of fully cavitating hydrofoils in a steady two-dimensional flow. The only boundary in the flow is that provided by the hydrofoil and its cavity. The cavity is always assumed to spring from the nose and trailing edge of the profile. The methods used are those of linearized inverse airfoil theory, in which one prescribes the pressure distribution on the wetted surface of the profile and then calculates its shape. The theory at zero cavitation number is considered anew in order to highlight the physical constraints involved in this inverse problem. However, major emphasis is given to basic procedures for profile design at nonzero or zero cavitation numbers. Optimum hydrofoil design is discussed from an engineering viewpoint.
Compression of a Viscoplastic Disk
Authors: Carlson R. L.
Published: November 2011

The similarities between the response of a viscoplastic material and the response of metals during forging are noted. The yield condition and flow law for an incompressible viscoplastic material are used as a basis for an approximate solution of the problem of the compression of a circular disk. The rate effects associated with the presence of time-dependent flow are observed to evolve as an integral part of the solution.
Measurement of Volume and Resistivity Changes in High-Pressure Experiments by an A-C Inductive Technique
Authors: Giardini A. A. , Poindexter E. H. , Samara G. A.
Published: November 2011

A coil wound on a sample core subjected to high pressures may be used to measure compressibility and electrical resistivity of the core. In a first approximation, the coil reactance reflects core volume, and the resistance reflects core resistivity. The exact impedance of the coil in the general case depends on the ratio of skin depth to sample size. With large skin depths, the sensitivity to volume changes is high, and with small skin depths, sensitivity to resistivity is high. Operation in these two cases was demonstrated for four materials of widely different hardness: barium, bismuth, titanium, and tungsten. In addition, operation was demonstrated at high temperatures by detection of the alteration of pyrophyllite to coesite plus kyanite. Permeability as a function of pressure was shown for an iron-nickel alloy. The chief advantage of the coil method is the remote, nonmechanical measurement of volume changes. In addition, it offers greater versatility to favor many different types of sample material.
Annulus Wall Boundary Layers in Axial Compressor Stages
Authors: Horlock J. H.
Published: November 2011

An analytical and experimental study is made of the development of secondary vorticities through the successive blade rows of a turbomachine. Whereas in cascade experiments the streamwise vorticity is usually zero at entry to the cascade, in the turbomachine this vorticity is in general nonzero and must be taken into account in the calculation of the secondary vorticity at exit from a blade row. In the calculation of boundary layer velocity profiles through an axial flow compressor stage, the variations in the exit air angles from the rows are computed first, from estimates of the secondary vorticities. There will always be overturning at the exit from the guide vane tip section, but tracing of the vorticity vectors through the machine shows that there may be underturning at rotor and stator tip. The exit air angles obtained from the analysis of these secondary flows may be used, together with actuator disk theory, to calculate axial velocity profiles in the boundary layers. It is suggested that this method of calculating the flow in the regions near the annulus walls should be used in the design of axial flow compressors.
On the Application of Zubov’s Method of Constructing Liapunov Functions for Nonlinear Control Systems
Authors: Szego¨ G. P.
Published: November 2011

The Liapunov second method is formalized in a set of theorems which yield to a stability criterion for nonlinear autonomous systems. Various procedures for constructing Liapunov’s functions by the Zubov method are discussed and several examples presented.
The Optimal Control of Some Attitude Control Systems for Different Performance Criteria
Authors: Flugge-Lotz I. , Marbach H.
Published: November 2011

Optimal control functions in the sense of minimum settling time and minimum fuel or energy consumption are derived for several different single-axis attitude control systems. The systems treated differ only in the mechanism used to produce control torque. The torque producing elements considered include, (i) reaction gas jets, with either one or two discrete levels of thrust, (ii) an armature controlled d-c motor, (iii) a two-phase a-c motor. Optimal switching curves for these systems are illustrated in the phase plane, and the optimal choice of system parameter values is discussed.
A Simple Iterative Procedure for the Identification of the Unknown Parameters of a Linear Time Varying Discrete System
Authors: Kushner Harold J.
Published: November 2011

A new “steepest descent” approach to the “adaptive control system” problem of the determination of the process dynamics of a time varying system is analyzed in considerable detail. The unknown parameters are the parameters of the impulse response of a linear discrete system. The identification procedure is a first-order iterative process and is designed to operate with the natural inputs of the system to be identified. After each new (single) input, new estimates of all the unknown parameters are computed. The method is computationally simple and, in its analysis, the effects of additive noise in the observations (of both input and output), random drift with time, or neglected parameters of the impulse response are handled with relative ease and become transparent. Time variations are taken directly into account, thus eliminating the necessity of the assumption of stationarity over a period of time.
Effects of Two-Dimensional, Sinusoidal Roughness on the Load Support Characteristics of a Lubricant Film
Authors: Burton R. A.
Published: November 2011

An analytical study is made of the effects of two-dimensional, sinusoidal roughness on pressure and shear stress in a lubricant film between two parallel plates engaged in steady, parallel, relative motion. The effects of pressure and heating upon viscosity, as well as shear elasticity are accounted for in the case where roughness height is small relative to film thickness. Second-order influences which contribute to net load support by the film are computed in terms of the first-order solution. The results give evidence as to when boundary roughness may be negligible in its influence on hydrodynamic film calculations. Most important, however, they give evidence of a type of instability which may contribute to film breakdown in some marginal lubrication situations.
A Theory of Self-Acting, Gas-Lubricated Bearings With Heat Transfer Through Surfaces
Authors: Kao Hsiao-Cho
Published: November 2011

Use is made of the continuity, Navier-Stokes, energy, and state equations to develop the differential equations for gas-lubrication problems. Heat transfer through the surfaces is allowed. The first approximation, not surprisingly, gives the Harrison equation which is usually obtained by assuming the isothermal process. The error introduced by this assumption is shown up in the second approximation, when the isothermal condition is dropped. Under normal operational condition, this error is small enough to be neglected. However, the main purpose of developing the second approximation is to allow heat transfer through the surfaces such that the load capacity can be increased. Two curves of the pressure distribution for the infinitely long inclined plane slider bearing at various bearing numbers are plotted to show the effect of a temperature difference compared with the isothermal case given by Harrison’s equation. These results suggest that merely by increasing the temperature difference between the surfaces, the load capacity of a self-acting, gas-lubricated bearing can be considerably increased.
The Pulsation Method for Generating Cavitation Damage
Authors: Plesset Milton S.
Published: November 2011

Results are presented for the cavitation damage of materials by a laboratory procedure in which the cavitation is applied in an intermittent, or pulsed, manner. It is found that the rate of damage in materials sensitive to corrosion is much greater for pulsed cavitation than for steady cavitation when the cavitating liquid is salt water. The damage rate is also increased by the pulsed cavitation for these materials when the cavilating liquid is distilled water but by a smaller amount than in the salt solution. For corrosion insensitive materials there is no significant difference between the cavitation damage rate when it is applied in a steady or in a pulsed manner.
An Investigation of the Mechanism of the Friction and Wear of Carbon
Authors: Midgley J. W. , Teer D. G.
Published: November 2011

A comparison has been made of the friction and wear characteristics of carbons of high (p = 0.1) and low (p = 0.9) graphiticity (hereafter referred to as graphitic and nongraphitic) in vacuo, air, and CO2 at ambient room temperature. The friction of nongraphitic carbon can be just as low as graphitic carbon and it is similarly affected by absorbed gases. It is different, however, in that it periodically exhibits a substantial increase of friction which is not normally observed with graphitic carbon. The surface orientation produced by rubbing is also quite different and so is the mode of wear. These differences have been investigated and are explained in terms of the different physical properties associated with the structures of the two materials. On the basis of this work a critical assessment has been made of the various theories concerning the mechanism of the friction of graphitic carbon. The results are in accord with the view that the low friction of graphitic carbon (and of nongraphitic carbon) is due to low adhesion between crystallites, not to the low shear strength nor to the separation of the surfaces by rolled up crystallites.
On the Prediction of Gas Flow Rates Through Round Wire Screens
Authors: Smetana Frederick O.
Published: November 2011

A relatively simple expression is derived for the flow through round wire screens by considering the screen to be made up of a number of noninteracting cylinders and using classical data on the drag coefficient of a cylinder at various Reynolds numbers and Mach numbers. The theory is found to agree closely with the result of some recent experiments for low solidity screens (0.5 or less). At Knudsen numbers higher than 0.01 the screen passes more mass than would be predicted by the theory. This is attributed to slip.
Minimum Time Control of Second Order Pulse-Width-Modulated Sampled-Data Systems
Authors: Polak E.
Published: November 2011

This paper treats the minimal time control problem for two second order pulse-width-modulated sampled-data systems, one with a double integrator type plant and one with a plant described by an integral and a time constant. Such plants are encountered in systems with hydraulic components. It is shown rigorously that for minimal time control the phase plane can be divided into two regions: a striplike region around the optimal switching trajectory for a continuous relay system with the same plants, in which the pulse width must be adjusted for optimal action; and the rest of the phase plane in which an optimal p.w.m. system of the type described behaves like a continuous optimal relay system, the pulse duration being equal to the sampling period. A brief description of an electromechanical computer capable of implementing minimal time control for these systems is also given.
Optimal Control Methods for On-Off Sampling Systems
Authors: Nelson W. L.
Published: November 2011

This paper considers the problem of optimal (minimum-time) on-off regulation of a dynamic plant whose state is known only at periodic instants of time. It is shown that on-off control inputs which change value only at the sampling instants inherently lack the capability of providing accurate (dead-beat) control. If, however, the on-off controller is modified to include pulse width control, it not only has the capability for accurate control, but also has the capability for optimal control comparable to that of a saturating amplifier controller. In addition, the optimal pulse width control inputs can be specified as a function of the state of the plant at each sampling instant. The application of this method is discussed in detail for the cases of pure inertial and second-order underdamped plants.
An Empirical Creep Law From a Single Test
Authors: Finnie Iain
Published: November 2011

A method is described by which an empirical creep law, relating stress, strain, and strain rate, may be obtained from a single constant-load creep test. An example to illustrate the method is given, and the empirical creep law is compared with the results of several constant stress creep tests.
Crack Propagation in Aluminum-Foil Laminates
Authors: Mote C. D. , Frisch J.
Published: November 2011

Crack propagation in 4 × 10-in. laminated specimens of 1100 H-19 aluminum foil under uniaxial tensile loads perpendicular to the crack direction has been investigated. While the crack behavior is similar to that found in monolithic sheets the laminates exhibit a brief arresting of crack growth before onset of sudden fracture. It was further established that the Griffith-Irwin energy-dissipation rate is a constant for any particular laminate configuration.
A Theoretical Method of Determining Discharge Coefficients for Venturis Operating at Critical Flow Conditions
Authors: Smith Robert E. , Matz Roy J.
Published: November 2011

A venturi designed to operate at critical flow conditions and to provide accurate measurement of flow rates of compressible fluids is described. A theoretical method of determining the discharge coefficients for this venturi is presented, and a comparison of the theoretically and experimentally determined coefficients for one venturi is shown (working fluid—air). The values of discharge coefficient were in the range of 0.992 to 0.994, and the theoretically and experimentally determined coefficients agreed within ±0.06 per cent over the range of conditions investigated.
The Schlieren Method Applied to Flow Visualization in a Water Tunnel
Authors: Bland Richard E. , Pelick Thomas J.
Published: November 2011

The adaption of the schlieren method for the purpose of observing flow in water is a recent development at the Garfield Thomas Water Tunnel. Flow is shown over an opening and over a semicylinder for a range of Reynolds numbers of 2.5 × 104 to 25 × 104. The relative effects of temperature and pressure as they affect the index of refraction are treated. The relative persistency of a temperature gradient in air and water is considered, and the relative effects in air and water of a chosen density gradient are calculated.
Preliminary Design of a Roll-Stabilization System for a Ship
Authors: Stallard David V.
Published: November 2011

The roll stabilization of a ship with servo-operated fins is analyzed as a system problem from the viewpoint of a control engineer. The preliminary design of a roll-damping system for a particular passenger ship is set forth. The roll-angle response to a sinusoidal sea-torque is analyzed, and the improvement made by the roll-damping system is evaluated. A rate gyro of good resolution and a damped pendulum are adequate for roll-sensing instrumentation. A preliminary design for a valve-controlled fin servo is made, but it is so wasteful of power that a pump-controlled fin servo is designed as an alternative. Energy aspects of control systems in general are considered briefly.
A Study of Theories of Fracture Under Combined Stresses
Authors: Cornet I. , Grassi R. C.
Published: November 2011

Experimental data are presented for a cast nodular iron and for high-silicon cast iron materials which represent limiting conditions of ductility in a test of fracture theories. Data of other pertinent investigations are reviewed and various failure theories are discussed with regard to their applicability. It is concluded that failure under combined stresses of brittle materials can be predicted adequately by applying a notch modified distortion energy criterion. However, other criteria are also applicable. Since criteria for the failure of brittle materials are conspicuously phenomenological, the application of solid state and dislocation theory, to explain the initiation and growth of a crack in a heterogeneous structure under combined stresses, has been discussed.
Dynamic Synthesis of Higher-Order, Optimum Saturating Systems
Authors: Kurzweil Fred
Published: November 2011

A new technique for the synthesis of optimum switching criteria for higher-order saturating systems is investigated in this paper. Basically, the technique consists of generating a linear switching criterion that is equivalent to the optimum switching criterion for each state of the system. Thus as a trajectory of the system is traced out, the optimum forcing function is determined point by point, resulting in the optimum trajectory for the system. The synthesis procedure has been proved experimentally by simulation of a third-order system on an IBM 797 digital computer.
The Volume of Stressed Material Involved in the Rolling of a Ball
Authors: Drutowski R. C.
Published: November 2011

The force necessary to roll a ball on a flat plate is experimentally determined as a function of the load for a number of different ball diameters and steel structures. Previously published data expressing rolling force as a power of the load and ball diameter are shown to be inadequate in describing the behavior of the rolling ball over the full-load range employed in this investigation. The rolling force is found to be negligible for contact stresses less than a certain “threshold” contact stress. Once the rolling force becomes measurable, it is shown to be proportional to the volume of significantly stressed material until a contact stress is attained which is sufficient to cause plastic deformation. The significantly stressed volume is determined from the distribution of the strain energy stored in the Hertzian stress field of a ball in contact with a flat plate. The threshold contact stress, the constant of proportionality between the rolling force and significantly stressed volume, and the contact stress at which plastic deformation is initiated are shown to be independent of the diameter of the rolling ball but dependent on steel structure. A model is introduced relating the volume of significantly stressed material to the elastic hysteresis processes responsible for the energy losses during rolling.
An Improved Analytical Solution for Self-Acting, Gas-Lubricated Journal Bearings of Finite Length
Authors: Ausman J. S.
Published: November 2011

An improved analytical solution designated the “linearized ph” solution is obtained for gas-lubricated journal bearings of finite length. Whereas the older first-order perturbation solution is useful for small eccentricity ratios (ε < 1/2), the linearized ph solution may be used for high eccentricity ratios. As such it permits estimation of ultimate bearing load capacity. The linearized ph solution is expressed in the form of simple corrections to the first-order perturbation solution, and as such can be computed quickly and easily.