bluuebunny/crossref_metadata_2025 huggingface dataset:
Method of force Defect Coefficients Applied to An Asymmetric Two-Dimensional Orifice
Authors: Begg R. D.
Published: February 2007

The method of force defect coefficients was developed by Jobson and improved by Bragg to calculate compressible discharge coefficients for axisymmetric orifices from the more easily computed or measured incompressible values. This method has been adapted to deal with two-dimensional flow, and the analysis for a particular case, that of compressible jet flow emerging from an asymmetric straight-sided orifice, has been completed.

Predictions of jet angle and thickness have been calculated for a range of orifices, and these are shown to compare well with experimental measurements.
Testing of Materials at Medium rates of Strain
Authors: Cooper R. H. , Campbell J. D.
Published: February 2007

The problems involved in the measurement of the mechanical properties of rate-dependent materials are discussed, with special reference to the role of the elastic stiffness of the testing machine and specimen.

A description is given of a newly developed universal testing machine, operated by hydraulic pressure and capable of testing at crosshead velocities up to about 40 in/s. The machine has been used in two ways: for tensile tests at approximately constant strain rates in the range 10-1 to 10-2 s-1; and for compression tests in which a load is applied in a few milliseconds and maintained at a nearly constant value while the specimen is plastically deformed.

The machine is instrumented so that the applied load and cross-head velocity are recorded throughout the test. The testing technique and the accuracy of measurement are discussed with reference to experimental results obtained in tests on annealed copper, mild steel, silicon-iron, and a high-strength aluminium alloy.
Transient Response of Beams
Authors: Bradshaw A. , Warburton G. B.
Published: February 2007

The response of beams to transient excitation applied through the supports is considered. A general method of analysis, based on the integral equation of motion, is developed, applicable to single-and multi-span beams; for non-uniform beams the conventional approximation of replacing the distributed mass by a number of discrete masses is made, and an equivalent matrix analysis is given. For all beams the response is obtained in terms of normal modes. Response spectra, dependent upon bending moment or stress, are given for various pulse shapes for simple beams, and it is shown that for single pulse excitation the maximum response depends primarily on the rise-time of the pulse and only marginally upon the shape of the pulse. The accuracy of approximate methods of determining response spectra is discussed. The effects on transient response of flexibility in the supports and of the support positions are considered. Application of the theory to an engineering system is discussed briefly.
Notation and General Equations for the Kinematics of Planar Mechanisms
Authors: Molian S.
Published: February 2007

This paper describes a notation for the kinematic properties of an assembly of co-planar laminae. Such an assembly may include a lamina capable of deformation in certain ways. The notation enables the user to write down a set of equations, called symbolic equations, which determine the movability of the assembly, or its degree of redundancy should it be a structure; and a further set called kinematic equations, which determine relative displacements, velocities and accelerations. Examples are given to show the use of the notation for the description of various mechanisms and the determination of their movability. A solution of the kinematic equations for a 4-bar linkage is given, and its use in analysis and design described. The use of this notation in the synthesis of linkages is discussed, and the possibilities of the single closed chain enumerated completely.
Natural Frequencies of Plate Systems using the Edge Effect Method
Authors: Dickinson S. M. , Warburton G. B.
Published: February 2007

In this paper the Bolotin edge effect method is used to consider the free flexural vibrations of systems built up from rectangular plates. The constituent plates of the systems are considered either to lie in the same plane and form part of a plate continuous over line supports or to lie in planes at right angles to each other, as in box constructions.

The application of the edge effect method to single-and multi-plate systems is described and the approximate frequency equations for two two-plate systems are given. The first 10 natural frequency parameters for these two systems for particular side ratios are compared with those obtained using a series solution and agreement is shown to be good. A few frequency parameters for a closed box computed using the edge effect method and the series solution are also compared.

The range of plate systems to which the edge effect method may be applied with complete success and the range to which it may be applied with only partial success are indicated.

The sources of errors in the edge effect solutions are indicated.
Distribution of Heat between Sliding Surfaces
Authors: Barber J. R.
Published: February 2007

When sliding takes place between metals of comparable hardness, the mechanism is probably restricted to single asperity interactions of a short duration. In this paper, a solution is derived for the heat conduction in a single interaction of this type and it is shown that, unless there is initially a temperature difference between the surfaces, there can be no meaningful distinction between ‘moving’ and ‘stationary’ surfaces. The solution is integrated for an arbitrary configuration and the result is considered with reference to the work of Jaeger (1)† and Blok (2).
Optimization of Vibration Absorbers: A Graphical Method for use on Idealized Systems with Restricted Damping
Authors: Falcon K. C. , Stone B. J. , Simcock W. D. , Andrew C.
Published: February 2007

Existing methods for the design of vibration absorbers can only be applied to limited types of system. In this paper, a graphical method is described which can be applied to a wider range of problems, in particular when the main system possesses damping and the absorber damping ratio is fixed.
Examination of Effective Rates of Combustion Heat Release in a Dual-Fuel Engine
Authors: Karim G. A. , Khan M. O.
Published: February 2007

The combustion processes in a dual-fuel engine are examined through the computation and analysis of effective rates of heat release. Methane was adopted as the primary fuel and the effect of deliberately introducing carbon dioxide along with the methane was also examined to simulate operation on methane sources containing carbon dioxide as a major contaminant. An examination of the various heat release records suggests that dual-fuel combustion generally appears to undergo two distinct phases. The first phase is associated mainly with the consumption of the pilot and some associated gaseous fuel, while the second phase is dependent on the concentrations and the quality of the gaseous fuel employed. Under light audible knock, the first phase gets prolonged and persists over a much longer period than under knock-free combustion. The rates of burning are excessively high and project well over the second phase. This is indirectly indicative of the auto-ignition nature of knock and the simultaneous rapid burning of the pilot together with a very substantial fraction of the gaseous charge.
Displacement Excitation of Vibrating Systems
Authors: Mahalingam S.
Published: February 2007

The response of a mechanical system to the displacement excitation at a support is determined in terms of the natural frequencies and modes of the rigidly supported system. Receptances in closed and series forms are obtained for torsional and flexural systems and their properties are discussed. Support receptances are used to determine the modal and frequency changes caused by the introduction of flexibility at a beam support. The case of a beam on two flexible supports is then analysed using the cross-receptances between supports.
An Analysis of the Plastic Interaction of Surface Asperities and its Relevance to the Value of the Coefficient of Friction
Authors: Edwards C. M. , Halling J.
Published: February 2007

Surface asperities are considered as wedge-shaped bodies which are plastically deformed wherever relative motion occurs between mating surfaces. This plastic interaction produces interfacial forces between the surface asperities which are considered, in the collective sense, to represent the total applied normal and tangential forces acting on the sliding surfaces. A solution is proposed which enables the values of the interfacial forces to be obtained at each time interval during the life history of a junction interaction. Furthermore, it is shown that the nature of these forces is markedly dependent on both the initial asperity geometry and on the nature of any surface films which may be present at the asperity interfaces. From such results it is possible to predict the macroscopic values of the coefficient of sliding friction. Such results suggest that an earlier solution due to Tabor should be considered as the special case for perfectly plane surfaces. The solution also indicates the nature of the plastic deformation of the asperities and displays the phenomena of junction growth. Furthermore, it is demonstrated that very large values of the macro-scopic coefficient of friction are associated with very strong molecular adhesion of the surface asperities particularly for materials having high ductility.
Experimental Study of the Plastic Interaction of Model Surface Asperities during Sliding
Authors: Edwards C. M. , Halling J.
Published: February 2007

The paper describes an experimental study of the plastic interaction of triangular shaped lead model asperities deformed under conditions of plane strain. The investigation yields values of the normal and tangential force variations throughout the junction interaction and details of the plastic deformation particularly in relation to junction growth. A number of asperity interfacial conditions are considered ranging from complete adhesion to very low shear strengths achieved using p.t.f.e. strip. The experimental results are compared with an earlier theoretical solution to this problem and show reasonable agreement with the theoretical predictions. In particular it is shown that the normal force, which is usually compressive, may become tensile for conditions of high adhesion between the asperities. This leads to very high values of the macroscopic friction coefficient such as occur in hard vacuum situations. The experimental results for the various surface conditions show sufficient agreement with theoretical predictions to justify the use of this type of theoretical approach for the wider study of the friction and wear of mating surfaces.
Theoretical Analysis for the Redrawing of Cylindrical Cups through Conical Dies without Pressure Sleeves
Authors: Fogg B.
Published: February 2007

A theory for the redrawing of cylindrical cups through conical dies is presented. In the absence of a pressure sleeve a zone of unconstrained drawing exists prior to the conical zone and the principle of minimum energy is used to establish the extent of the zone and the associated deformation and stresses. A linearization of the von Mises yield criterion for plane stress problems is adopted and use of the flow rule associated with this criterion allows the variation of thickness across an element to be taken into account in the solution of the stress equilibrium equation; the strains can also be determined without resorting to numerical integration. Because the deformation during redrawing takes place in a series of discrete steps, work-hardening can be conveniently included in the analysis. Bending and unbending contribute significantly to the process work and a more detailed examination of the mechanism is justified. The present theory allows the effects of friction, die angle and die intersection radius to be examined but the punch load/redrawing ratio relation has been considered for only one die profile and clearance. The results for the redrawing of 70/30 brass cups with and without interstage annealing are compared with experimental redrawing loads and whilst excellent agreement exists for the near-limiting redrawing ratios, the theory considerably over-estimates the punch loads at the smaller ratios. A possible reason for the difference is discussed.
Random Vibrations in Discrete Nonlinear Dynamic Systems
Authors: Bhandari R. G. , Sherrer R. E.
Published: February 2007

A one-degree-of-freedom system and a two-degree-of-freedom system containing Dis-placement and velocity dependent nonlinearities subjected to stationary gaussian white noise excitation have been studied by the method of the Fokker-Planck equation. Non-linearities have been represented by suitable polynomials. The Fokker-Planck equations governing the stationary probability density function for these systems have been solved by representing the density function by a multiple series of Hermite polynomials. The constants in the series expansion were determined by Galerkin's method. Analysis is developed for the system containing nonlinearities described by suitable polynomials in velocity and displacement dependent forces. Comparisons were made between series and exact solutions for those special cases for which exact solutions are known.
Parametric Excitation of a Non-Homogeneous Bernoulli-Euler Beam
Authors: Francis P. H.
Published: February 2007

In this paper is considered the problem of the stability of the parametric response of a simply supported Bernoulli-Euler beam having an elastic modulus that varies continuously and monotonically throughout its length. The beam is excited by axial harmonic forces applied to the ends. The Galerkin procedure is used, which, in the first approximation, leads to a single Mathieu equation representing the stability regions for an equivalent uniform beam having averaged properties. For the second and higher approximations, the co-ordinate functions used in the Galerkin procedure couple, leading to a coupled system of Mathieu equations. Results from the first and second approximations are compared with, a view toward establishing the degree of non-homogeneity for which the first approximation predicts the instability regions with acceptable accuracy. It is shown that for moderate non-homogeneities, such as might be introduced by thermal sources, the first approximation leads to results of quite tolerable accuracy. In an Appendix are presented some computed data for the free vibrational frequencies of the non-homogeneous beam under static end forces.
Minimum Vibration Cam Profiles
Authors: Kwakernaak H. , Smit J.
Published: February 2007

The problem of finding cam profiles with limited follower velocity, acceleration and jerk and minimal residual vibrations over a prescribed range of cam speeds is formulated as a mathematical optimization problem. Two versions of the problem are considered: a quadratic problem formulation and a linear programming formulation. Numerical solutions have been found through the use of a digital computer and the methods are compared. Examples of profiles are presented which compare favourably with the well-known cycloidal profile.
Lateral Vibration of a Pipe Conveying a Fluid
Authors: Naguleswaran S. , Williams C. J. H.
Published: February 2007

The lateral vibration of a pipe conveying a fluid is investigated theoretically and experimentally. An exact solution for the natural frequency, axial distribution of phase and modal envelope is computed for a pinned-pinned, fixed-fixed and pinned-fixed span. Approximate one and two term Galerkin, Rayleigh-Ritz and Fourier series solutions are obtained and compared with the exact solution. It is found that a two term Galerkin or Rayleigh-Ritz solution is simple to evaluate and provides a good estimate of frequency and phase. The influence of axial tension and internal pressure is included.

The experimental results are in agreement with theory at low flow speeds but show the difficulty of accurate buckling flow speed prediction.
Dynamic Stresses in Free-Pinned Beams during Impact with a Stop
Authors: Deas K. W.
Published: February 2007

Bending stress expressions are derived using standard vibration methods for impact of the free end of a free-pinned beam on a rigid and a spring stop and these are shown for any cross-section shape to be independent of beam length or dimension of cross-section. Test results are presented suggesting confirmation of theory.
An Expression for the Coefficient of Velocity of Venturi-Meters
Authors: Elagib A. A. R.
Published: February 2007

Venturi-meters often have to be used in conditions different from those at which they have been calibrated or at conditions under which experimentation is not usually feasible, e.g. in hot-water feed pump systems or for large water flows. An attempt to give a simplified theoretical expression for venturi coefficients of velocity is being made. Such a theoretical expression would be augmentative or give a useful alternative to experiment.
Measurement of High Gas Temperatures with Fine Wire Thermocouples
Authors: Bradley D. , Matthews K. J.
Published: February 2007

The recent advent of reliable thermocouple pairs of high melting point has provided new capabilities for high temperature gas measurement. The errors involved in such measurements using fine wire thermocouples are dependent upon radiation from the wire, conduction to the main leads, and convection to the wire. These are all discussed, together with methods for calculating the appropriate corrections. Some numerical results are presented.
An Equation of State for Compressed Water from 1 to 1000 Bar and from 0°C tO 150°C
Authors: Gibson M. R. , Bruges E. A.
Published: February 2007

The precision with which the thermodynamic properties of compressed water and steam are known has led, not unnaturally, to the development of equations of state suitable only for use on electronic digital computers. The equations are in the main empirical although some are highly sophisticated and lead to lengthy programs and complex sub-routines. Among such equations are those of the 1966 and 1967 Formulations of the Thermo-dynamic Properties of Ordinary Water Substance prepared by the International Formulation Committee of the International Steam Conference. The favoured form of equation has been one in which the dependent variables are enthalpy, volume and entropy and the independent variables pressure and temperature. However, this form of equation may not prove to be always the most suitable and the purpose of this paper is to describe how another type of equation, in which the dependent variable is enthalpy and the independent variables are pressure and entropy, may be established and applied. It is believed that this particular type of equation, relating as it does the three most important parameters in pump and turbine performance, has special qualities for design and efficiency calculations. By way of example the efficiency of a water turbine is evaluated according to the ‘thermodynamic method’ described by Thom (2). A concluding section outlines the further steps being taken by the authors to provide a similar type of equation over ranges of pressure and temperature up to 1000 bar and 1000°C.
Some Fracture Mechanics Correlations
Authors: Pook L. P.
Published: February 2007

The results of tests on two high-strength steels, beryllium copper and perspex, together with some published data on high-strength steels were examined to see whether there was any relationship between the fracture mechanics parameter K1C and conventional mechanical properties. It was found that for steels and beryllium copper a correlation appeared to exist between K1C and the zero gauge length strain (= Z/(1 - Z) where Z is the reduction of area measured in a tensile test). It was also found that for constant, K1C was proportional to the square root of Young's modulus. The correlation band for steels was too wide for K1C to be estimated accurately from.
Two-Phase Critical Flow through Suction Slots in Low Pressure Steam Turbine Blades
Authors: Ryley D. J , Parker G. J.
Published: February 2007

As part of an investigation to study the removal of water from the trailing edge of a low pressure steam turbine fixed blade by suction slots, experiments were made on a perspex test section in which a 1-in wide section of the suction slot was simulated.

The flow characteristics are considered of the passage in the choked condition and a comparison is made with some two-phase critical flow theories. The theories are briefly presented and discussed, and the relevant formulae given. It is found that the homogeneous-equilibrium model grossly underestimates the discharge rates whilst all of the other flow models overestimate by at least 30 per cent.
Coupled Bending-Bending Vibrations of Pre-Twisted Cantilever Blading Treated by the Rayleigh-Ritz Energy Method
Authors: Dawson B.
Published: February 2007

The Rayleigh-Ritz method is used to determine the natural frequencies and mode shapes of vibration of pre-twisted rectangular cross-section beams. The method is dependent upon a good choice of approximating functions for the dynamic deflection curves. In the present analysis, series of the characteristic functions representing the normal modes of vibration are taken as the approximating functions for the bending displacements in the directions of the co-ordinate axes. The choice of this particular series leads to a considerable reduction in the number of elements in the final matrix equation and also considerably reduces the computing time.

The natural frequencies of vibration are obtained for various width-to-thickness ratio beams with pre-twist angle in the range 0-90°, and the mode shapes of vibration are presented for one particular width to thickness ratio beam. The results are compared to results obtained by other methods and to experimental results, and good agreement is shown to exist.
Effect of Secondary Injection on the Characteristics of a Supersonic Parallel Diffuser
Authors: de Dedman A. S. Forge , Martin B. W.
Published: February 2007

This paper reports further progress in evaluating the performance of the supersonic parallel diffuser incorporating a sudden entry enlargement which provides for the injection of secondary fluid. The effects of introducing proportions up to 10 per cent of the primary flow in a two-dimensional diffuser are illustrated by schlieren photographs of the flow patterns and by measurements of the local wall static pressure and heat transfer distributions. The normal and oblique shock regimes (corresponding respectively to the unstarted and started conditions) are modified by the strengthening of the weak shock system generated at the primary nozzle mouth. Optimum overall static pressure recovery is reduced by the admission of secondary fluid, though the conditions under which it is achieved remain unchanged unless forced injection is used. The local heat transfer no longer follows the static pressure distribution and in the unstarted diffuser large peaks occur near mid-length. Over an intermediate range of Reynolds number the mean heat transfer is greater than that without secondary flow but otherwise it is less.
Fretting Fatigue Failure in Friction Grip Bolted Joints
Authors: Spiers R. , Cullimore M. S. G.
Published: February 2007

Fatigue tests on a large number of double cover plate butt joints showed that the cause of failure in the majority of cases was by cracks originating in an annular area of fretting damage around the bolt hole. The nature of the fretting is discussed and the variation with load amplitude of the size of the annular area is described. Several well defined patterns of fatigue cracking were observed. These are described and their associated crack origins classified and related to the joint geometry and load levels.
Film Cooling Slots: The Importance of Lip Thickness and Injection Angle
Authors: Sivasegaram S. , Whitelaw J. H.
Published: February 2007

Measurements of adiabatic-wall effectiveness in a two-dimensional, constant-property flow are reported for a slot of fixed height but with two different slot-lip thicknesses. The results confirm the trends exhibited by earlier measurements of the impervious-wall effectiveness which showed that the ratio of slot-lip thickness to slot height, t/yc, is an important parameter in determining the effectiveness of film cooling. The effectiveness is shown to decrease significantly as t/yc is increased beyond a value of 0·25; for lower values, the influence is dependent upon the ratio of slot to free-stream velocities.

The influence of the injection angle has also been investigated and measurements of the adiabatic-wall effectiveness are reported for angles of 30, 60 and 90 to the direction of the free-stream. These measurements agree qualitatively with the measurements of Papell but show quantitative differences.
Experimental Behaviour of Thin-Walled Cylindrical Shells Subjected to External Pressure
Authors: Montague P.
Published: February 2007

The paper describes external radial and hydrostatic pressure tests on 12 mild steel, thin-walled cylindrical shells. Radial deflections and surface strains on the inside and outside of the cylinders' walls are related to the conventional small deformation theory. The elastic deformation patterns are found to be similar in shape to the lobar modes which can be predicted by elastic instability theory. The collapse pressures of the shells and their modes of failure are considered in relation to the rigid-plastic theory, the importance of initial imperfections is discussed and an attempt is made to relate the geometric and material properties of the cylinders to modes of failure and to appropriate collapse analyses.
Flow Disturbances Due to Blade Thickness in Turbomachines
Authors: Lewis R. I. , Horlock J. H.
Published: February 2007

Variations of blade thickness from hub to casing of a turbomachine, which impose a non-uniform blockage upon the meridional flow, often give rise to significant perturbations. In the first part of this paper this effect is simulated by considering the circumferential average of the source distributions required to represent the blade profiles. In the second part the equations of fluid motion are first averaged across the blade passage and the resulting equations solved for the averaged properties.

Similarity between the differential equations obtained in these two ways is noted. A number of analytical examples are discussed and a simple experimental result is reported.
Acoustic and Internal Damping in Uniform Beams
Authors: Johnston R. A. , Barr A. D. S.
Published: February 2007

Experimental results on the overall damping of freely supported uniform beams of circular and rectangular section are reported. These results show that the loss factor is, beyond a certain stage, highly frequency dependent but that this dependency largely disappears when the experiment is carried out in vacuo. The frequency dependency is shown to be due to acoustic radiation from the beam. Theoretical results using an approximate theory for rectangular sections agree well with the observed values. Over a certain frequency (wavelength) region the acoustic damping may be many times the internal damping of the beam for the material tested (mild steel).
Presentation of Elastohydrodynamic Film-Thickness Results
Authors: Greenwood J. A.
Published: February 2007

Yet another set of dimensionless variables is offered. These have the advantage of the Blok groups, that all results can be plotted on a single graph, but in addition one group is of secondary importance, so that all results lie in a narrow band. Thus, film thickness is shown to depend primarily on a single parameter.

It is deduced that the extrapolated rigid cylinder theories give a very good estimate of the film thickness under elastohydrodynamic conditions.
Noise and Flow Characteristics of Coaxial Jets
Authors: Williams T. J. , Ali M. R. M. H. , Anderson J. S.
Published: February 2007

The noise from cold subsonic coaxial jets issuing from concentric nozzles with external mixing has been examined and an attempt made to relate the results to the flow patterns of the jets. As the velocity of the annular jet was increased in relation to a given central jet velocity, an initial attenuation of the jet noise was observed. On further increasing the annular jet velocity until the velocities of the two streams were nearly equal, the noise was in excess of that of the central jet alone. An attempt has been made to predict the curve relating the attenuation attained to the coaxial jet velocity.

In comparing the attenuation produced by a coaxial jet combination with that of a single jet, it could be argued that the total thrust in each case should be the same and experimental results are presented on this basis. Results are also available for a nozzle configuration in which the jets are mixed internally in a tube before discharge, and the paper is completed with the results obtained from an annular nozzle acting alone.
A Study of Six-Speed Gear Trains with Eight Gears
Authors: Sanger D. J. , White G.
Published: February 2007

It is shown that six-speed gear trains with the minimum number of gears, i.e. eight gears, can be divided into categories which are suitable for overdrive ratios or speed reduction ratios. One gear train from each category is examined and its characteristics and design limits discussed. A technique for computing solutions is outlined and a few typical solutions are given.
Strategy for Cross-Bores in High Pressure Containers
Authors: Cole B. N.
Published: February 2007

It is frequently necessary to drill a cross-bore through the wall of a cylindrical pressure vessel, and it tends to be taken for granted that the cross-bore—itself of circular section— should lie along a diameter of the main cross-section. The weakening effect of such a hole is well known, and reduces the safe working pressure down to 2/5 of the value for the undisturbed cylinder in the case of a Tresca material, or nearly down to 1/3 in the case of a von Mises material. The paper shows how it is possible to reclaim a large proportion of the ‘lost’ pressure capacity by use of a cross-bore which is either elliptical in section, or, more conveniently, round but offset from a diametral centre-line. Such procedure could thus also greatly improve the fatigue life of the pressure vessel.
Pre-Stressing Effects in Band-Reinforced Pressure Vessels
Authors: Miatt B. B. , Cole B. N.
Published: February 2007

In investigating the elastic interactions between a cylindrical shell and successively added turns of band reinforcement applied under tension, the paper has a twofold purpose. Firstly, it sets out to determine the magnitude of the stress relaxation in the winding after many further turns have been added, and shows that this can be considerable. Secondly, it investigates the extent to which a not uncommon neglect of this relaxation can reduce the safe working pressure of a band-reinforced pressure vessel. While the reduction is found to be relatively minor, it is shown that a simple calculation can provide due correction.
Detailed Analysis of a Two-Stage Four-Way Electrohydraulic Flow-Control Valve
Authors: Nikiforuk P. N. , Ukrainetz P. R. , Tsai S. C.
Published: February 2007

A detailed analysis is given of a flow-compensated, two-stage, four-way, closed-ports electrohydraulic flow-control valve. Factors considered in the analysis of the first stage include: the electromagnetic forces generated by the torque motor, impedance of the motor coil, inertia of the flapper, viscous damping forces, spring forces, pressure feedback forces, and leakage flow. Factors considered in the analysis of the second stage include the acceleration force on the spool, viscous friction forces, restraining spring forces, flow reaction forces, leakage flow, and the compressibility of the oil.

Experimental verification of the analytical work is included.
Control Forces in Rocket Nozzles Produced by a Secondary Gas Stream Inclined at Various Angles to the Nozzle Axis
Authors: Neilson J. H. , Gilchrist A. , Lee C. K.
Published: February 2007

The side force produced by the injection of secondary gas into the supersonic regime of a main nozzle is investigated with particular reference to the effect of the angle between the secondary jet and the main nozzle axis. In the experiments, downstream and upstream injection angles at one secondary port location in the main nozzle were examined. It is shown that there is a definite advantage to be gained by injecting the secondary gas in an upstream direction. An analytical analysis of the results indicates that for moderate secondary mass flows maximum side force is produced when the angle between the axis of the secondary port and the normal to the axis of the main nozzle is in the range 40-50°. When injecting a given secondary mass flow at the angle for maximum side force the axial thrust augmentation is almost zero. As the angle of injection is reduced from upstream values to downstream values the side force reduces and the thrust augmentation increases, indicating that thrust augmentation can be used to determine how effectively a given mass flow of secondary fluid is being utilized in the production of side force.
Effects of Hydraulic Forces in Annular Pressure Seals on the Vibrations of Centrifugal Pump Rotors
Authors: Black H. F.
Published: February 2007

In centrifugal pumps, the annular clearance spaces of the leakage path, i.e. impeller seals and balance piston seals, act as powerful hydrostatic bearings with turbulent flow. In the present discussion, the dynamic forces due to these bearings acting on the rotor are analysed, including the effect of squeeze action, i.e. the effect of velocities of separation or approach of the bearing and journal surfaces.

Synchronous forced whirling is analysed in a simple idealization comprising a single mass rotor, including the estimation of amplitudes as well as critical speeds. Large damping forces due to squeeze action are found, in qualitative agreement with experimental work by Marcinkowskij and Karincev (3)†. A simplified treatment of the effects of fluid rotation is included in the analysis of rotor vibrations, leading to an analysis of high speed whip instability onset.
Optimization of Vibration Absorbers: Application to Complex Structures
Authors: Stone B. J. , Andrew C.
Published: February 2007

This paper describes a method for designing a vibration absorber, incorporating polymer spring/damping elements, for attachment to a complex main system. The point of attachment can be remote from the position(s) of interest in the main system, for which any characteristic of absolute or relative receptance can be considered.

Tests on a machine tool show that butyl rubber provides an effective and convenient damper material, even with main systems already possessing a high level of vibration damping, and that the addition of an absorber can effect a considerable improvement in the predicted performance of the machine. The addition of more than one absorber is likely to provide greater improvements.
Experimental Aerodynamic Coefficients in the Analytical Study of Suspension Bridge Flutter
Authors: Scanlan R. H. , Sabzevari A.
Published: February 2007

Certain coefficients are designated, in the analytical formulation of the suspension bridge flutter problem, to provide for the aerodynamic forces of incipient flutter. A method is given for evaluating these coefficients through observation of wind tunnel model vibratory response under steady wind. Use of the method successfully reproduces the classical flutter aerodynamic coefficients of an aerofoil. When flutter coefficients are obtained by it for a model of the original Tacoma Narrows bridge, the method successfully predicts the incipient torsional flutter characteristic of this well-known structure. The paper also discusses the roles of model and prototype damping and the aerodynamic representativeness of section models relative to the full bridge.
Cumulative Damage in Fatigue: A Step towards Its Understanding
Authors: Brook R. H. W. , Parry J. S. C.
Published: February 2007

A method is described which uses changes of apparent dynamic modulus and damping during fatigue cycling, for estimating accurately the fatigue lives of stainless steel (Rex 535) specimens. This technique for estimating well in advance of failure the fatigue lives of individual specimens avoids the usual difficulties caused by scatter of fatigue results, and has enabled a more precise quantitative investigation to be made of cumulative fatigue damage (i.e. damage due to multi-level loading) than would have been possible using conventional experimental methods. By estimating the remaining life of a specimen at one stress amplitude before measuring the equivalent remaining life at a second stress amplitude by cycling to failure, it was possible to determine lines of equal damage on a plot of stress amplitude versus remaining fatigue life. These lines of equal damage were used to predict the fatigue lives of specimens subjected to programmes of multi-level loading, and the accuracy of these estimates, when compared with the subsequent experimental results, is much better than has been achieved hitherto. Depending on the stressing programme chosen, Miner's linear damage rule is shown to be very good, rather pessimistic, or very dangerous.
Flow Deflection by Gauze Screens
Authors: Reynolds A. J.
Published: February 2007

A mathematical model is set up to predict the deflection of a flow passing obliquely through a plane gauze. It differs from existing descriptions in accounting consistently for velocity variations in the deflecting flow, and in relating the deflection at the gauze to the total deflection in a more realistic way. The deflection at the gauze is specified in two ways, as being half the total, and as equalling the total. These two relations are found to represent the performance of gauzes whose solidities are, respectively, less than and greater than one-half. Formulae are developed which predict the flow deflection with good accuracy for these two régimes.
A Simplified Presentation of Equations for the Thermodynamic Properties of Dichlorodifluoromethane, CCl2F2 (Refrigerant-12)
Authors: Haywood R. W.
Published: February 2007

The paper commences with a general treatment illustrating the advantages of writing the equation of state of a pure substance in characteristic (canonical or fundamental) form, from which expressions for all other thermodynamic properties can be written down in terms only of the characteristic function and its partial derivatives. In this way, thermodynamic consistency between the equations for the different properties is automatically ensured.

The initial difficulties in constructing an equation of state in characteristic form are briefly discussed, and it is shown how the characteristic equation may be built up from an existing p-v-T equation of state and an equation for the specific heat capacity at zero pressure.

An existing set of equations for the single-phase region of Refrigerant-12 is transformed in this way into a single characteristic equation of state from which, through given simple expressions, all other thermodynamic properties may be computed. The equation of state is expressed dimensionlessly in reduced co-ordinates so that it may be used with equal facility in any coherent system of units. For the sake of completeness, other existing equations for the saturation pressure and for the saturated liquid have been put into dimensionless form and are given in the paper.
Thermal Conductivity of Steam at Atmospheric Pressure
Authors: Brain T. J. S.
Published: February 2007

In this paper work carried out by the author to measure the thermal conductivity of steam at atmospheric pressure in the temperature range 100-700°C is reported. This work was undertaken in view of the discrepancies which exist in the experimental data at atmospheric pressure. In particular, the serious differences which exist at the high temperatures between the results of Russian experimenters, who give higher values than those given by American and German workers, needed investigation.

Utilizing two concentric cylinder cells an absolute steady state method has been used to measure the thermal conductivity of steam in the temperature range 100-700°C, at atmospheric pressure, with a probable accuracy estimated to be within ± l·5-±2 per cent.

The results obtained confirm Russian observations at the higher temperatures and it is hoped that these results will help finally to resolve the inconsistencies in the experimental data. A fresh assessment of all the experimental data is given by the author where arguments in favour of both the lower and higher atmospheric lines are discussed. A new correlation of experimental data has been undertaken and a reduction in the tolerances put on the equation defining the atmospheric line from ±3 per cent in the range 100-400°C and ±4 per cent in the range 400-700°C to ±2 per cent over the complete range 100-700°C is now recommended.
Acoustical Analysis Applied to Internal Combustion Engine Exhaust Systems of Conical Form
Authors: Nassif M. H.
Published: February 2007

In the following analysis the variation of the charging capacity of a small two-stroke motor-cycle engine is utilized to assess the non-steady flow characteristics of conical exhaust pipes having different length and divergence.

The performance of the engine under the most favourable conditions is applied to determine the natural frequency of exhaust ducts fitted with conical portions.

The experimental data yielded are compared with theoretical computations based on acoustical treatments and inspection of the results obtained supports the conclusion that the ports behave as a partly, and not as a fully, closed end as commonly accepted.
A Review of Theories of Metal Removal in Grinding
Authors: Wetton A. G.
Published: February 2007

In recent years, increasing interest in the mechanics of grinding as a metal cutting process has resulted in a considerable step forward in understanding the fundamental parameters, though no complete solution is yet available. Much is now known about the shape of the abrasive grits, the nature of their cutting edges, and how these are affected by the various wear mechanisms prevailing during grinding to produce sharp cutting edges by fracture, or dulled abrasive by chemical or attritious wear. Using this information experiments using sliding single grits, and models of single grits, have demonstrated the importance of considering both forward and lateral flow of metal, and have shown the differences from conventional metal cutting. Chip formation in the conventional manner is seen to occur and metal is also removed as slivers, resembling chips, from the side walls of grooves resulting from lateral metal flow. The influences of speed, friction, lubrication and grit distribution need to be more closely examined, however, before the experimental results of grinding simulation can be accurately assessed.
Reference Stress for Redistribution Time in Creep of Structures
Authors: Bill I. M. , Mackenzie A. C.
Published: February 2007

When creep occurs in a structure subject to a step load the stresses redistribute with time. It is shown that if the initial stress distribution is the linear elastic one, and the material obeys an n-power creep law, the time for a particular stress to reach its steady state value may be estimated from the results of a single creep test at a selected value of stress with-out the parameters of the creep law being known. This reference stress is identified from the results of an appropriate elastic-creep analysis.
Sub-Surface Fatigue Strength of a Steel
Authors: Bray P. F.
Published: February 2007

Rotating bending fatigue tests on En 40B steel gave a fatigue limit for surface failure of 30·5 tonf/in2. With nitrided test-pieces sub-surface failures were produced and, with no allowance being made for residual stresses, a fatigue limit of 34·5 tonf/in2 was obtained for sub-surface failure. In the absence of residual stresses this fatigue limit would probably have been higher.
Pure Design Method for Aerofoils in Cascade
Authors: Murugesan K. , Railly J. W.
Published: February 2007

An extension of Martensen's method is described which permits an exact solution of the inverse or blade design problem. An equation is derived for the normal velocity distributed about a given contour when a given tangential velocity is imposed about the contour and from this normal velocity an initial arbitrarily chosen blade shape may be successively modified until a blade is found having a desired surface velocity distribution. Five examples of the method are given.
Effects of the Different Temperature Scales on the Calculation of the Thermodynamic Properties of Water Substance
Authors: Gibson M. R.
Published: February 2007

Attention is drawn to the fact that the derivation of so-called ‘Thermodynamic Temperatures’ by the addition of the quantity, 273·15, to temperatures referred to the IPTS leads to discrepancies in the values of the thermodynamic properties calculated from equations of state by means of the thermodynamic relations. These differences are shown to be significant when compared with the tolerances in the 1963 International Skeleton Tables and a simple method of avoiding this error is described.
Choice of Origin for Body Axes Attached to a Rigid Vehicle
Authors: Bishop R. E. D. , Parkinson A. G.
Published: February 2007

The equations of motion of a rigid vehicle are derived in terms of body axes whose origin does not coincide with the centre of mass of the vehicle. The application of the results to the linear analysis of the motion of ships and aircraft is explained. An example is given of the effects of the mass centre being off-set from the origin in calculating oscillatory coefficients from test results obtained with a planar motion mechanism.
Overcut, a New Theory for Tip Interference in Internal Gears
Authors: Polder J. W.
Published: February 2007

For over forty years internal gears were surrounded by obscurity occasioned by the discovery of tip interference where calculation suggested that it would not occur (1)†. The present author developed a new theory for tip interference which gave better insight in the manufacturing process.

Internal gears not satisfying rule (12) will be injured by the cutter at a centre distance still too low for involute generating. This injuring phenomenon in an early stage of cutting is called overcut. The overcut has to be neutralized by an increase of the tooth spaces to such an amount that the final generating centre distance is larger than existing theories suggested. When rule (12) is satisfied, then there is no overcut and no tip interference.
Role of Surface Degradation Film on the Tractive Behaviour in Elastohydrodynamic Lubrication Contact
Authors: Poon S. Y.
Published: February 2007

A new phenomenon on the tractive behaviour in an elastohydrodynamic lubrication contact, associated with a surface degradation layer formed after severe shearing, is described.
Control Forces in Rocket Nozzles Produced by Multiport Gaseous Injection
Authors: Neilson J. H. , Gilchrist A. , Lee C. K.
Published: February 2007

This work is concerned with the optimization of the method by which secondary gas is used to produce side force in rocket nozzles and is part of a series of investigations in which the effects of secondary port area, port location in the main nozzle and the angle between the axes of the main and secondary nozzles have been studied. In this note the merits of using multiport configurations for introducing the secondary gas as compared with using a single port of equivalent area are considered. It is shown that, at a given location for introducing the secondary flow, multiport arrangements of either the radial or parallel type give side forces less than that produced by a single port passing the same secondary mass flow.