bluuebunny/crossref_metadata_2025 huggingface dataset:
Subultimate Prestrain and Aging in Mild Steel
Authors: Felbeck D. K. , Gibbons W. G. , Ovens W. G.
Published: November 2011

Room-temperature tensile straining of mild steel followed by aging at 350 F causes return of the upper yield and a raising of the stress-strain curve. Tensile tests on a special rimmed steel of low Mn/C ratio show not only the expected raising of the stress-strain curve, but raising by an additional amount when several small increments of strain are each followed by aging at moderate temperatures. Longitudinal tensile prestrain by rolling gives substantially the same results. Tests of specimens prestrained in a limited region by impact or in slow tension and aged indicate that embrittlement of the whole specimen may result. The combined theories of Griffith and Orowan, plus an extension of the Ludwik triaxiality concept, can provide a consistent description of the local stress and average stress (energy) criteria that are necessary and sufficient for high-speed low-energy fracture to occur.
Design and Operation of Aeration Test Stand for Testing Turborotors of High Specific Speed
Authors: Koeller P. , Newey R. A.
Published: November 2011

The outside shroud surfaces of hydraulic turborotors, such as turbines, pumps, and pump-turbines are subjected to parasitic fluid drag by the liquid in the band and crown chambers. If air is injected into the shroud chambers, displacing the liquid there, the shroud friction diminishes. To study the flow mechanisms required to maintain the air economically in the band chambers of high-specific-speed turborotors, the test stand described herein was designed and operated in the laboratories with which the two authors are associated.
Characteristics of Herringbone-Grooved, Gas-Lubricated Journal Bearings
Authors: Vohr J. H. , Chow C. Y.
Published: November 2011

A differential equation is obtained for the smoothed “overall” pressure distribution around a herringbone-grooved, gas-lubricated journal bearing operating with a variable film thickness. The equation is based on the limiting case of an idealized bearing for which the number of grooves approaches an infinite number. A numerical solution to the differential equation is obtained valid for small eccentricities. This solution includes the case where the journal is undergoing steady circular whirl. In addition to the usual plain bearing parameters L/D, Λ, and whirl speed ratio ω3/(ω1 + ω2), the behavior of a grooved bearing also depends on four additional parameters: The groove angle β, the relative groove width α, the relative groove depth H0, and a compressibility number, Λs, which is based on the relative speed between the grooved and smooth members of the bearing. Results are presented showing bearing radial force and attitude angle as functions of β, α, H0, Λs, Λ, and whirl speed ratio.
On the Mechanics of Non-Newtonian Media
Authors: Tipei N.
Published: November 2011

The extension of Newton’s shearing law is aimed at the tensions being expressed by means of a general type equation. The case of the Bingham type media is considered and the components of the tensions tensor for homogeneous isotropic bodies are obtained in an orthogonal system of coordinates. The notion of viscosity is also extended by the introduction of viscosities of any order n, having the dimensions (M/L)Tn−2. The equation of motion upon any direction xi is then derived, extending thus the Navier-Stokes equations. Further the particular cases of incompressible fluids and steady motions are considered. Applications to simple cases are performed: The motion in tubes, coaxial cylinders, or between solid parallel surfaces. These applications lead, as particular forms of the general formulas obtained, to result in good agreement with those found by other authors (Paslay and Slibar, Milne, and so on). The flow between parallel plates is studied too, for different shearing laws. Finally, a more general form of the shearing stresses is considered and by the proposed generalization, the possibility of a direct unitary study of various continuous bodies of a great practical importance is obtained.
Fretting Corrosion Caused by Vibration With Rolling Bearings Stationary
Authors: Pittroff Hans
Published: November 2011

If nonrotating rolling bearings are exposed to vibration then the raceways especially in roller bearings can be damaged in a short time. False brinelling in bearings is caused by fretting corrosion. All research in this area therefore belongs to the field of fretting corrosion. Owing to the alternating elastic deformation in the contact area between the rolling elements and the raceway as well as to the shearing strength being exceeded in the microcontact area, surface particles are abraded, which become immediately oxidized. The kind and the extent of damage primarily depend on the static load of the bearings. The resistance to false brinelling can be increased by means of lubricants and surface treatments. It is possible to give limits for the admissible flute characteristics. In cases of already known vibration characteristics the time of the bearing failure can be mathematically predetermined.
The Role of Microslip for Freely Rolling Bodies
Authors: Drutowski R. C.
Published: November 2011

The energy required to roll a sphere in a cylindrical groove is shown to be partly a hysteresis loss and partly a microslip loss. Data for three different sphere-groove combinations are separated into the two types of losses by comparison with data for toroid-plane rolling combinations chosen to give identical stress fields. The microslip loss is accounted for by the Palmgren-Heathcote equation assuming a coefficient of sliding friction of 0.073. Once the microslip torque is subtracted from the total rolling torque, the remaining torque turns out to be proportional to the load and independent of the geometry of the rolling elements, which includes various diameter spheres in addition to the combinations mentioned previously.
Performance of a Small-Sized, Critical Flowmeter Assembly
Authors: Dye D. E.
Published: November 2011

Measurement of low mass-flow rates was readily accomplished by development of two similar flowmetering assemblies. Each assembly consisted of five 0.016 to 0.070-in. diameter critical-flow nozzles and individual control valves connected between common inlet and exit manifolds. Mass-flow rates through each nozzle were determined over a range of upstream pressure and temperature. The probable deviations in the measured data are approximately ≠0.83 percent. Discharge coefficients were calculated from the calibration results using the well-known one-dimensional critical-flow equation. An average error of ≠2.5 percent in the discharge coefficient is possible because of the difficulty in determining true throat areas of these small-sized nozzles.
ASME Research on High Pressure-High Temperature Steam and Water Flow Measurement: Report of Subcommittee 7 of the ASME Fluid Meters Research Committee
Authors: Murdock J. W.
Published: November 2011

This paper describes the results of an ASME sponsored research program on the measurement of high pressure-high temperature steam and water flows. Results obtained during tests at three central stations, a steam and water laboratory, and three hydraulic laboratories are described. It was determined that coefficients of ASME orifices or nozzles are within a tolerance of 1 percent of ASME coefficients providing that the beta ratios were limited to a maximum of 0.60 for nozzles and 0.65 for orifices and that materials are selected so that the surfaces remain in an essentially as new condition, and frequent inspections are made to verify surface and cleanliness.
An Investigation of Self-Acting Foil Bearings
Authors: Ma J. T. S.
Published: November 2011

Experimental results on the interior and the exit region film-thickness measurements of self-acting foil bearings are presented and discussed. These measurements were made with capacitive sensors and conductive foils. The measured and predicted values agree very well within the range of nondimensional parameters, h0/R, from 10−4 to 10−3 and, T/μU, from 105 to 106. The agreement deviates for values beyond these ranges. Empirical expressions for predicting the constant and minimum film thickness applicable beyond these ranges are also presented. They are valid within the range of h0/R from 5(10)−5 to 10−2 and T/μU from 104 to 105. Growing sinusoidal film thickness in the exit region was also observed, measured, and checked with theoretical predictions.
A Behavioral Model for the Fracture of Surface Hardened Components
Authors: Ebert L. J. , Krotine F. T. , Troiano A. R.
Published: November 2011

An analytical model has been developed which shows that the fracture of surface hardened components initiates at the subsurface interface because of the triaxial stress-state developed at this location.
Externally Pressurized Foil Gas Bearings
Authors: Barlow E. J.
Published: November 2011

An axisymmetrical gas foil bearing is analyzed, with the foil being treated as a thin plate bent into a cylindrical shape. Symmetrically placed, circumferential, constant pressure sources supply the lubricant.
The Load Capacity of Short Journal Bearings With Oscillating Effective Speed
Authors: Gupta B. K. , Phelan R. M.
Published: November 2011

The development of the Reynolds equation for the general case of dynamically loaded journal bearings is extended to include the concept of an effective speed that combines in one term the angular velocities of the journal, bearing, and load. Numerical solutions for the short-bearing approximation are presented for the case of an oscillating effective speed and a load that is constant or varying sinusoidally. Results are compared with available experimental data. The major conclusion is that for those cases involving an oscillating effective speed and a reversing load, the only significant contribution to load capacity comes from the squeeze film and the wedge film can safely be ignored when designing such bearings.
Lubrication Review: Developments in Bearings and Lubricants—A Digest of the Literature From 1961–1962
Authors: Shevchenko R. P. , Reichenbach G. S. , Roberts M. , Kingsbury E. , Ramadanoff Dimiter , Wojtowicz W. J. , Hartung H. A. , Derner W. J. , Ryffel H. H. , Du Bouchet A. , Sibley L. B. , Wehe R. L. , Ku P. M. , Cuellar J. P.
Published: November 2011

This 1961–1962 lubrication digest reviews developments in fluid-film and rolling-element bearings, lubrication for bearings, gears, and automobiles; and covers basic work done in the general areas of friction and wear; elastohydrodynamic, boundary, and full film lubrication; and lubricant properties. The authors cover specific areas of lubrication literature and it is recommended that the reader, even the specialist, peruse related areas since the years of effort in this field have exposed more of the fundamentals; and the conclusious drawn, and the basic laws formulated in one area are important to all areas. It is wistfully hoped that the digest will disclose disproportionate effort because of funding and imbalance between empirical and theoretical work and spur corrective action.
Stability of Subharmonic Oscillations in Nonlinear Systems
Authors: Oldenburger Rufus , Nicholls Robert E.
Published: November 2011

This paper presents a method for finding necessary conditions such that a subharmonic oscillation may exist in certain types of nonlinear feedback systems. The method is applicable to feedback systems with one, instantaneous, nonmemory-type, nonlinear element. Equations are derived giving the fundamental output of a nonlinear element when forced by two sine waves of integer ratio frequency. Normal describing-function assumptions are made with regard to attenuation of higher-order harmonics. An example of a system incorporating a perfect relay is presented. The results of the analysis have been verified experimentally on the analog computer.
Analysis of Piecewise Linear Systems by the Method of Integral Equations
Authors: Shen C. N. , Wang Hubert
Published: November 2011

Analysis of piecewise linear systems may require the solution of high-order linear differential equations whose parameters are constants within a given region but change into different constants for adjacent regions. The multiple regions of such a system may be identified with discrete intervals and it is a simple matter to obtain the system response by the method of integral equations. These solutions are given in the form of convergent infinite series, the terms of which may be easily evaluated by a digital computer. The time interval of each region is found by substituting successive values of these truncated series until the required boundary conditions are satisfied. The method is applied to a third order-type two system whose sustained oscillation, when subjected to dry friction, is to be eliminated by dead-zone compensation. The system has four regions with different parameters for each region of the differential equations which are converted into Volterra integral equations of the second kind. The variables are iterated within the digital computer until a convergent solution is found for the condition of sustained oscillation. Procedures are given to determine critical values of dead zone for various ramp rates at which the system is stable.
A Solution to the Sampled, Minimum-Time Problem
Authors: Koepcke R. W.
Published: November 2011

A solution of the linear, sampled, minimum-time problem is developed which permits the determination of the control policy in real time by an on-line digital control computer. The solution is illustrated by means of two examples.
The Finite Magnetohydrodynamic Journal Bearing
Authors: Kuzma D. C.
Published: November 2011

An analysis of a finite journal bearing is presented for the case of an electrically conducting fluid in the presence of a radial magnetic field. The magnetohydrodynamic form of the two-dimensional Reynolds equation is derived and solved numerically for the pressure distribution. The load-carrying capacity and torque are determined from the pressure distribution. Numerical data for nonconducting bearing surfaces are compared with the data from the ordinary journal bearing. It is shown that the load-carrying capacity and torque are increased by the application of the magnetic field.
An Approximate Numerical Scheme for the Theory of Cavity Flows Past Obstacles of Arbitrary Profile
Authors: Wu T. Yao-Tsu , Wang D. P.
Published: November 2011

Recently an exact theory for the cavity flow past an obstacle of arbitrary profile at an arbitrary cavitation number has been developed by adopting a free-streamline wake model. The analysis in this general case leads to a set of two functional equations for which several numerical methods have been devised. Some of these methods have already been successfully carried out for several typical cases on a high-speed electronic computer. In this paper an approximate numerical scheme, somewhat like an engineering principle, is introduced which greatly shortens the computation of the dual functional equations while still retaining a high degree of accuracy of the numerical result. With such drastic simplification, it becomes feasible to carry out this approximate numerical scheme even with a hand-computing machine.
Dynamic Indentation Using Rigid Slow Speed Conical Indenters
Authors: Johnson W.
Published: November 2011

Rigid conical indenters of various weight, of half angle 30, 45, 60, and 75 deg were made to impinge normally on blocks of duralumin, copper, and lead at various speeds. Among other things the resulting indentation diameter is shown to be related to the velocity at impact raised to approximately the power 2/3. The experimental results here reported confirm those of previous workers but interpretation of them is different.
A Liquid-Medium Step-Function Pressure Calibrator
Authors: Smith R. O.
Published: November 2011

Some characteristics of a step-function pressure calibrator of the type devised by D. P. Johnson and J. L. Cross of NBS have been investigated. Theoretical prediction of the wave generation appears to be impracticable. It has been found possible, by empirically determined adjustments, to produce monotonic step functions having 95 percent rise times in about 10 millisec suitable for calibration of transducers. Calibration accuracies are around 5 to 7 percent. The monotonic step-function pressure is also useful in evaluating creep or hysteresis in high frequency transducers which previously could not be inspected for that characteristic.
Reactor-Vessel Design Considering Radiation Effects
Authors: Porse L.
Published: November 2011

Nuclear-vessel design involves consideration of changes in metal properties resulting from fast-neutron irradiation effects. This paper outlines precautions and design steps which can cope with these effects and insure safe operation of PWR closed-cycle-type reactor vessels for their planned life expectancy. Illustrations show workable stress levels as a function of temperature for the reactor-vessel material in nonirradiated and irradiated condition. A plot of equivalent pressure temperature relationships is shown as a guide for the plant operator during plant start-up and shutdown periods.
Rotating Stall in a Radial Vaneless Diffuser
Authors: Jansen W.
Published: November 2011

This paper is concerned with the theoretical and experimental aspects of unsteady flow in a radial vaneless diffuser. Specifically, the appearance of self-excited oscillations of large amplitude is investigated in great detail. The waves appear when the angle between the tangential and total velocity becomes very small. The predicted wave speed and perturbed velocity distribution versus radius agree quite well with the experimentally obtained values, however, an undeterminable constant appears in the equation which describes the disturbed velocity distribution. A stability criterion indicates that such pulsating flow can occur if and only if there is a region of radially inward flow. The hypothesis is proposed that the waves are a result of the interaction of the three-dimensional boundary layer near the side walls and the free stream. Unsteady flows of this type can be linked to unstable centrifugal pump, blower, or compressor operation.
On the Starting Characteristics of Supersonic Ejector Systems
Authors: Addy A. L. , Chow W. L.
Published: November 2011

The transient pumping characteristics of supersonic ejector systems are investigated both theoretically and experimentally. The theoretical analysis of this transient problem is based on quasi-steady flow concepts. The steady-state ejector analysis, upon which the present study must be based, considers the basic interaction between the primary and secondary streams as well as the viscous mixing effects which are the predominant flow mechanism at small secondary flow rates. The results of applying this steady-state analysis to the present problem are presented and shown to be in excellent agreement with experimentally observed ejector starting characteristics.
Visual Cavitation Studies of Mixed Flow Pump Impellers
Authors: Wood G. M.
Published: November 2011

Three mixed flow impellers representing a wide range of design parameters were tested in a closed water loop to obtain correlations of the high-speed photographic records of the cavitation formations with various performance parameters. It was found that cavitation existed for all impellers at much higher values of NPSH than those associated with a finite drop in the impeller head rise. The cavitation formations in the vane channels of the impellers were observed to be cyclic in nature, whereas the cavitation near the leading edge of the vanes was more stable.
Flow in a Pipe Following an Abrupt Increase in Surface Roughness
Authors: Logan Earl , Jones J. B.
Published: November 2011

Measurements of velocity, turbulence intensity, and Reynolds stress distributions following a sudden increase in surface roughness of a pipe are reported. The wall shear stress increases abruptly to its final value and the pressure gradient is very nearly constant throughout the transition region. Reynolds stresses throughout much of the transition region reach values exceeding those in fully developed flow in the rough pipe. The need for knowledge of shear stress distributions for use in the calculation of velocity distributions is pointed out. A flow model is suggested.
Flow in the Entrance of a Tube
Authors: Campbell William D. , Slattery John C.
Published: November 2011

The original development by Schiller for flow in the entrance of a tube is corrected to account for viscous dissipation within the boundary layer. The result is the best over-all description of velocity within the tube entrance currently available.
Gas Lubricated Spherical Bearings
Authors: Pan C. H. T.
Published: November 2011

The gas lubricated hemispherical bearing is considered theoretically. First, the isothermal Reynolds’ equation for a thin film between arbitrary curved surfaces is derived. The equation is then applied to a hemispherical bearing. External pressurization is considered by assuming a “point” source at the pole. The self-acting effects are studied by a perturbation analysis assuming a small displacement ratio of the journal center. Extension to moderate values of displacement ratios is treated by means of the linearized ph method. Numerical results for comparison with other bearing configurations and an earlier analysis are given.
Experimental Investigation of the Minimum Oil-Film Thickness in Spur Gears
Authors: Dareing D. W. , Radzimovsky E. I.
Published: November 2011

As a pair of gears is loaded, the minimum oil-film thickness between the gear teeth decreases and can approach a magnitude equal to the magnitude of the surface roughness. Metal-to-metal contact then occurs between the microscopic peaks on both mating teeth surfaces. Therefore, the minimum thickness of the film separating the mating teeth surfaces may be considered as one of the criteria of capacity for a gear drive. A testing technique that was developed for measuring oil-film thickness between loaded gear teeth while running is presented in this paper. The voltage drop across a thin oil film that is required to cause an electrical discharge was used to determine the oil-film thickness. A specially designed machine containing a planetary gear train was used in these experiments. The relationships between the minimum oil-film thickness and the load transmitted by the gearing under certain conditions were determined using this method.
On the Crack Extension in Plates Under Plane Loading and Transverse Shear
Authors: Erdogan F. , Sih G. C.
Published: November 2011

The crack extension in a large plate subjected to general plane loading is examined theoretically and experimentally. It is found that under skew-symmetric plane loading of brittle materials the “sliding” or the crack extension in its own plane does not take place, instead crack grows in the direction approximately 70 deg from the plane of the crack. This is very nearly the direction perpendicular to the maximum tangential stress at the crack tip, which is 70.5 deg. The hypothesis that the crack will grow in the direction perpendicular to the largest tension at the crack tip seems to be verified also by cracked plates under combined tension and shear. In spite of the fact that “sliding” and “tearing” modes of crack extension do not take place in brittle materials it is shown that one can still talk about critical stress intensity factors in plane shear and transverse bending of plates. It is also shown that, in general plane loading, the fracture criterion in terms of stress intensity factors is an ellipse.
A Critical Analysis of Crack Propagation Laws
Authors: Paris P. , Erdogan F.
Published: November 2011

The practice of attempting validation of crack-propagation laws (i.e., the laws of Head, Frost and Dugdale, McEvily and Illg, Liu, and Paris) with a small amount of data, such as a few single specimen test results, is questioned. It is shown that all the laws, though they are mutually contradictory, can be in agreement with the same small sample of data. It is suggested that agreement with a wide selection of data from many specimens and over many orders of magnitudes of crack-extension rates may be necessary to validate crack-propagation laws. For such a wide comparison of data a new simple empirical law is given which fits the broad trend of the data.
Linearized ph Stability Theory for Translatory Half-Speed Whirl of Long, Self-Acting Gas-Lubricated Journal Bearings
Authors: Ausman J. S.
Published: November 2011

The linearized ph approximation to the time dependent Reynolds equation is solved simultaneously with the equations of motion for a rotating journal shaft supported by a rigidly mounted bearing sleeve. Given the two bearing parameters Λ=6μωR2paC2 and Ω=MCω2πpaDL a critical operating eccentricity ratio is determined below which the bearing is unstable and above which the bearing is stable. Whirl frequency at the threshold point is computed to be equal to or slightly less than one-half rotor speed.
The Theory of Resonance in Hydropower Systems. Discussion of Incidents and Accidents Occurring in Pressure Systems
Authors: Jaeger Charles
Published: November 2011

The opinion has been expressed that—in the past thirty years—the most severe and spectacular accidents have been caused by resonance in power conduits. If this appraisal is true, then there is a gap in our knowledge to be filled. The purpose of this paper is to summarize the actual knowledge of this particular chapter of practical fluid mechanics and to open the way to more advanced research.
Optimizing Control of Single Input Extremum Systems
Authors: Frait John S. , Eckman Donald P.
Published: November 2011

The idea of direct optimization is briefly presented and an introduction given to the divider-optimizer. By investigation of the operating principles of the divider-optimizer, it is shown that the divider functions can be accomplished in separate and distinct manners. The optimizing behavior of the modified form of the divider-optimizer is investigated in the optimization of two quite different dynamic optimal systems. Experimental results of an analog computer study are presented. It is also shown that the modified form of the optimizer presents the possibility of a more flexible optimizing control using simple, reliable, and relatively inexpensive components.
Notch Rupture Behavior as Influenced by Specimen Size and Preparation
Authors: Couts W. H. , Freeman J. W.
Published: November 2011

A notch-sensitive forging was tested at 1300 F to measure the effect of machining practice and of limited variations in Kt and specimen size upon notch rupture life. Within the limits studied, specimen size appeared predominant. A discontinuity was observed in the dependence of notch life upon stress.
Plastic Analysis of the Instability of Pressure Vessels Subjected to Internal Pressure and Axial Load
Authors: Felgar R. P.
Published: November 2011

Future advances in rocket engine-case design are aimed at exploiting the capabilities of new high-strength steels. One mode of failure of such pressure vessels occurs due to plastic instability. This paper presents the results of analyses of the plastic instability behavior of pressure vessels made of Ladish D6A C steel using three methods of analysis of varying degrees of refinement. The Mises flow rule and associated flow equations are used to analyze the instability conditions for three ratios of the axial to the circumferential stress: 1/2, 1, 2. The results of the analysis are compared with experimental data. The most precise method of analysis which includes the elastic strain gives instability pressures which agree with experiments with errors of less than 3 1/2 per cent.
Deformation of Uranium Under Constant Load and Cyclic Temperature
Authors: Merckx K. R. , Wheeler K. R.
Published: November 2011

Tests were conducted on uranium under constant load and cyclic temperature. The work reported was different from earlier tests in that longer periods were used for the temperature cycle.
Flow Over an Inclined Plate
Authors: Abernathy F. H.
Published: November 2011

A free-streamline theory for an inclined flat plate in an infinite flow field, at an arbitrary angle of attack, is presented. Measurements of the location of the free-vortex layers, of the vortex-street frequency, and of the pressure behind an inclined sharp-edge plate are reported as a function of both the angle of attack of the plate and the lateral constriction of the flow. The separation between free-vortex layers is found experimentally to be essentially independent of lateral flow constriction. A form of the Strouhal number, using this separation distance as the characteristic flow dimension, is shown to be independent of lateral constriction of the flow and of the inclination of the plate.
Review of Critical Flowmeters for Gas Flow Measurements
Authors: Arnberg B. T.
Published: November 2011

Critical flowmeters for accurately measuring the mass flow rates of nonreacting real gases were reviewed. Discussions were presented on theoretical flow functions, on parameters for correlating discharge coefficients, and on the importance of real gas properties. The performance characteristics of critical nozzles and orifices of several designs were reviewed. Approaches were discussed to problems which must be researched before the fullest potential of this type of flow measurement can be realized.
Design and Calibration of the Lo-Loss Tube
Authors: Hooper Leslie J.
Published: November 2011

A low-loss and low-coefficient metering element has been devised and its operating characteristics determined under various conditions. The design was found to be not unduly sensitive to cavitation. The effects of installation have been evaluated for a short radius elbow and a tee. A partly open butterfly valve could be located 1 1/2 throat diameters downstream from the throat piesometers with an effect not exceeding 1/2 per cent upon the coefficient. Finally, the effects of pipe roughness and converging or diverging pipe can be correlated with the velocity distribution just upstream of the metering element.
The Optimum Response of Full Third-Order Systems With Contactor Control
Authors: Flu¨gge-Lotz I. , Titus H. A.
Published: November 2011

This paper presents an extension to the problem discussed in previous papers by Irmgard Flu¨gge-Lotz and Mih Yin.2, 3 In the full third-order problem it was found desirable to modify the iteration procedure used in the periodic approximation method that was developed in solving the optimum problem of the second-order, velocity-controlled system.2 A number of examples illustrate the new method. The examples were first constructed in reverse time by employing the true optimum switching times satisfying the optimum switching function, equation (6), which was developed by the methods of Pontrjagin.2 The final values of error and error derivatives which are obtained give the initial values for testing the approximate method. Periodic approximations of the optimum switching times are then obtained. It was found that for less than three switchings the approximate method leads to identical results. Reasonably small differences occur when three or more switchings are needed to reduce the initial disturbance to zero.
Reconsideration of the Annulus Flow Problem in Axial Turbomachinery
Authors: Mellor G. L.
Published: November 2011

The theory pertaining to the annulus flow problem in axial turbomachinery is reviewed and a simplified analysis which is essentially concerned with the effect of streamline curvature is worked out. Some generalized results are obtained for the case of a single blade row and for the oscillating flow between repeating blade rows of arbitrary spacing. The effect of finite blade width is assessed. The simple radial equilibrium hypothesis which is still attractive to designers is reconsidered and a modified radial equilibrium theory which directly eliminates the oscillatory terms is proposed as being more accurate and simpler than the conventional radial equilibrium theory.
Viscosity and Boundary Effects in the Dynamic Behavior of Hydraulic Systems
Authors: Cohen Hirsh , Tu Yih-O
Published: November 2011

The use of hydraulic mechanisms in low-energy transfer and information-transmittal devices requires a working understanding of dynamic hydraulic behavior. In this paper the effects of fluid viscosity and wall interference on wave motion in a simple hydraulic device are considered. It is shown that for the applications considered these phenomena may be treated by boundary-layer methods. Calculations are carried out to show their effect on piston displacement, and these effects are compared with the behavior when viscosity is not taken into account.
Microplastic Strain Hysteresis Energy as a Criterion for Fatigue Fracture
Authors: Feltner C. E. , Morrow Jo Dean
Published: November 2011

In this paper an energy criterion for fatigue failure is postulated. Microplastic strain hysteresis energy is considered to be an index for fatigue damage. On this basis, a relation is developed between stress amplitude and the number of cycles to failure which utilizes only material properties obtained from the static true stress-strain tension test. The analysis is found to compare well with an experimentally determined S-N curve for SAE 4340 steel.
Design of Optimum Multivariable Control Systems
Authors: Lee E. B.
Published: November 2011

The design of optimum controllers is considered for processes which are described by linear differential equations with one or more independent forcing terms. After presentation of a general method for designing what is usually a nonlinear controller, applications are made to: (a) Design of minimum energy controllers, (b) design of minimum response time controllers [1], and (c) design of minimum error controllers. Various other design criteria and restrictions on controller parameters are also discussed.
New Results in Linear Filtering and Prediction Theory
Authors: Kalman R. E. , Bucy R. S.
Published: November 2011

A nonlinear differential equation of the Riccati type is derived for the covariance matrix of the optimal filtering error. The solution of this “variance equation” completely specifies the optimal filter for either finite or infinite smoothing intervals and stationary or nonstationary statistics. The variance equation is closely related to the Hamiltonian (canonical) differential equations of the calculus of variations. Analytic solutions are available in some cases. The significance of the variance equation is illustrated by examples which duplicate, simplify, or extend earlier results in this field. The Duality Principle relating stochastic estimation and deterministic control problems plays an important role in the proof of theoretical results. In several examples, the estimation problem and its dual are discussed side-by-side. Properties of the variance equation are of great interest in the theory of adaptive systems. Some aspects of this are considered briefly.
Lubrication at High Temperatures With Vapor-Deposited Surface Coatings
Authors: Baldwin D. J. , Rowe G. W.
Published: November 2011

An experimental study of the friction of metals which have been coated with inorganic films by reaction with their surrounding atmosphere. The specimens are first cleaned at high temperature in vacuo and then heated in the selected reactive vapor. Many coatings will prevent seizure and give a fairly constant but high coefficient of friction up to high temperatures. Layer-lattice compounds such as MoS2, CrCl3, and TiI2 give much lower friction at all temperatures below those at which the film decomposes or evaporates (about 850 C for molybdenum disulphide). A film of boron nitride formed on boron shows a high intrinsic friction, but this can be reduced by certain vapors or by raising the temperature above about 800 C. Most of the experiments were performed with very light loads but the films are shown to be effective under kilogram loads. A simple indentation test capable of selecting lubricants under loads up to 12 tons is described. This shows that a film formed by heating stainless steel in CCl2F2 will lubricate at 400 C when the steel is deformed by over 50 per cent.
Perturbation Solutions for Gas-Lubricating Films
Authors: Gross W. A. , Zachmanoglou E. C.
Published: November 2011

Perturbation solutions for large and for small bearing numbers are developed and applied to steady, self-acting, infinitely long, journal and plane wedge films. Bearing films of this type develop load capacity as a consequence of relative surface motion. The solutions given here have validity for all ranges of geometrical parameters. Four-place accuracy in determining the load carried by a journal bearing is achieved. The plane wedge film solution for large bearing numbers is complicated by the reduction in order of the limiting equation. A boundary-layer type analysis yields fairly accurate results.
Grease Lubrication Studies With Plain Journal Bearings
Authors: Bradford L. J. , Barber E. M. , Muenger J. R.
Published: November 2011

Grease-lubricated plain bearings will operate with relatively low coefficients of friction and low lubricant consumption as shown by an experimental investigation on 3 1/2-in.-diam bearings. Formation of a “rheodynamic” load-carrying film; evidence of thixotropic behavior; and effects of variation of load, speed, clearance, feed rate, and lubricant properties are demonstrated.
Air-Hammer Instability in Pressurized-Journal Gas Bearings
Authors: Licht Lazar
Published: November 2011

A stability analysis is developed for gas journal bearings having externally pressurized pads, symmetrically spaced along the circumference. Simplifying assumptions are made and equations of flow and motion are stated in terms of perturbation quantities. The case considered is when the journal, initially in an eccentric equilibrium position, begins to move in an arbitrary direction under the influences of a small, random disturbance. Methods of factorizing and simplifying the characteristic determinants are shown, with the objective of reducing the work of examining the roots of characteristic equations. Special cases, such as the bidirectional thrust bearing and that of the journal initially in concentric position are discussed. Numerical and semiexperimental procedures of determining the coefficients of characteristic equations are outlined. Stability tests are suggested. Bearing parameters affecting stability are discussed.
The Magnus Effect: A Summary of Investigations to Date
Authors: Swanson W. M.
Published: November 2011

The Magnus force on a rotating body traveling through a fluid is partly responsible for ballistic missile and rifle shell inaccuracies and dispersion and for the strange deviational behavior of such spherical missiles as golfballs and baseballs. A great deal of effort has been expended in attempts to predict the lift and drag forces as functions of the primary parameters, Reynolds number, ratio of peripheral to free-stream velocity, and geometry. The formulation and solution of the mathematical problem is of sufficient difficulty that experimental results give the only reliable information on the phenomenon. This paper summarizes some of the experimental results to date and the mathematical attacks that have been made on the problem.
Squeeze Films: A Finite Journal Bearing With a Fluctuating Load
Authors: Hays Donald F.
Published: November 2011

A general method is derived for the solution of the Reynolds equation including the effects of tangential and normal velocities. It is applied to the solution of a full journal bearing under a fluctuating load with no journal rotation. The characteristics of a finite journal bearing under a cyclic sinusoidal load are shown in curve form.
A Preliminary Study of Turbulence Characteristics of Flow Along a Corner
Authors: Gessner F. B. , Jones J. B.
Published: November 2011

In the turbulent flow of a fluid along a corner, secondary flows occur which have a marked influence on the velocity distributions in planes normal to the mean flow direction. All published explanations of the cause of these secondary flows deal with the turbulent structure of the flow. In this paper, measurements of isotach patterns and directional turbulence intensities in the corner of a rectangular channel with zero pressure gradient and a range of free-stream turbulence intensity of 0.8 to 2.3 per cent are reported. (An isotach is a constant velocity line in a plane normal to the mean flow direction.) Within the range of variables investigated, the following conclusions are drawn: (a) Isotach patterns are essentially independent of free-stream turbulence intensity; (b) at any point the ratio of turbulence components in orthogonal directions in a plane normal to the mean flow direction is a maximum for directions tangent and normal to the isotach at that point; (c) the ratio w′/v′, where w′ and v′ are turbulence components, respectively, tangent and normal to the isotach at any point, is always greater than unity; and (d) in the vicinity of the bisector of the corner angle the ratio w′/v′ increases with increasing isotach curvature.
Some General Considerations in Process Optimization
Authors: Box G. E. P.
Published: November 2011

Problems of process optimization and in particular automatic optimization are currently being approached from many different directions. Investigations in process control and instrumentation, studies in statistical methods for the design of experiments for obtaining optima, studies on noise spectra and on numerical maximization subject to restraints as represented by linear and nonlinear programming, all throw light on the directions in which we must advance.
The Inception of Cavitation on Isolated Surface Irregularities
Authors: Holl J. W.
Published: November 2011

The inception of cavitation on isolated surface irregularities imbedded in a turbulent boundary layer is investigated experimentally and theoretically. Two families of cylindrical roughness elements having constant cross sections are studied. One family has a circular-arc cross section. The other family has a triangular cross section and was selected to simulate the separating flow which is typical of an actual surface irregularity. The theoretical minimum-pressure coefficient for the circular-arc irregularities is determined as a function of the relative height of roughness for several values of the boundary-layer shape parameter. Cavitation tests in the water tunnels of the Ordnance Research Laboratory on roughness elements ranging from 0.002 to 0.5 in. in height indicate that the incipient-cavitation number of an isolated surface irregularity is dependent upon the relative height of roughness, the boundary-layer shape parameter, the velocity, and other variables as yet unknown.
A New Approach to Linear Filtering and Prediction Problems
Authors: Kalman R. E.
Published: November 2011

The classical filtering and prediction problem is re-examined using the Bode-Shannon representation of random processes and the “state-transition” method of analysis of dynamic systems. New results are: (1) The formulation and methods of solution of the problem apply without modification to stationary and nonstationary statistics and to growing-memory and infinite-memory filters. (2) A nonlinear difference (or differential) equation is derived for the covariance matrix of the optimal estimation error. From the solution of this equation the co-efficients of the difference (or differential) equation of the optimal linear filter are obtained without further calculations. (3) The filtering problem is shown to be the dual of the noise-free regulator problem. The new method developed here is applied to two well-known problems, confirming and extending earlier results. The discussion is largely self-contained and proceeds from first principles; basic concepts of the theory of random processes are reviewed in the Appendix.
Bang-Bang Versus Linear Control of a Second-Order Rate-Type Servomotor
Authors: Meyfarth Philip F.
Published: November 2011

A simple nonlinear scheme for controlling a second-order rate-type servomotor is described. This scheme is referred to as “bang-bang” control since the input to the servomotor is made to “bang” from its maximum value in one direction to its maximum value in the other direction depending only on the sign of an error signal. This bang-bang system oscillates in a continuous high-frequency, low-amplitude limit cycle. The nature of this limit cycle is studied by the describing function approximation and by an exact method. The step and frequency response characteristics of the bang-bang system are discussed and compared with the characteristics of a simple linear system. It is shown that many aspects of the behavior of the bang-bang system can be predicted from rather simple considerations.
Estimating the Roots of the Characteristic Determinant for Multicoupled Systems
Authors: Lees S. , Felsenthal H. D. , Goldberg E. M.
Published: November 2011

A procedure is developed, based on Couchy’s residue theorem, for bounding the undamped natural frequency, damping ratio, and real part of the roots of the characteristic determinant associated with a multicoupled system with several inputs and outputs. The method can lead to a locus of the roots as one or more parameters are varied. The underlying theory is developed and a numerical illustrative example is included.
Hydrostatic Gas Bearings
Authors: Laub John H.
Published: November 2011

Orifice-regulated hydrostatic gas bearings offer significant advantages for instrument applications. In particular, gimbal bearings for inertial guidance systems can be designed with negligible starting torque and high stiffness, and for operation at extreme temperatures. A literature search revealed the lack of convenient and accurate data for the design of hydrostatic gas bearings of various configurations, taking into consideration the effects of compressibility, which cannot be neglected at higher pressures. Based on Euler’s equation, expressions for the significant parameters, i.e., pressure profile, gas-flow rate, gap height, and load-carrying capacity of pad and step bearings, are developed. These parameters yield results which are in excellent agreement with experimental data. The test fixture incorporates pneumatic loading by means of a bellows-suspended piston which is prevented from cocking by an air bearing.
A General Theory for Elastically Constrained Ball and Radial Roller Bearings Under Arbitrary Load and Speed Conditions
Authors: Jones A. B.
Published: November 2011

A completely general solution is obtained whereby the elastic compliances of a system of any number of ball and radial roller bearings under any system of loads can be determined. Elastic yielding of the shaft and supporting structure are considered as well as centrifugal and gyroscopic loading of the rolling elements under high-speed operation. The solution defines the loading and attitude of each rolling element in each bearing of the system as well as the displacement of each inner ring with respect to its outer ring. For ball bearings the precise location of the load paths in each raceway are found. Life estimates can be more accurately made since the fatigue effects can be evaluated over known paths in the raceways. The solution, which is accomplished numerically by iterative techniques, has been programmed for an IBM-704 digital computer.
A Sommerfeld Solution for Finite Bearings With Circumferential Grooves
Authors: Fedor J. V.
Published: November 2011

A method of solution is developed that circumvents the algebraic complexity in the solution of Reynolds differential equation applied to full journal bearings. The method leads to equations for journal-bearing characteristics that are in finite form. Salient features of the complete-oil-film solution are: As the eccentricity ratio b approaches 1, the load capacities of all finite bearings approach that of the infinite bearing; also, the friction curve intercept, (r/c)f, is 1 for all finite bearings when b equals 1. Results are compared with calculated values published by Muskat and Morgan for 0 < b < 0.6. Excellent agreement is found throughout the compared range.