bluuebunny/crossref_metadata_2025 huggingface dataset:
Conformity of Circular-Arc Gears
Authors: French M. J.
Published: February 2007

The conformity of circular-arc profile gears of the Wildhaber-Novikov sort is examined. It is indicated that the contact area may be a banana shape rather than the ellipse hitherto assumed. Two consequences of this are that too small a difference between the profile radii may reduce the useful conformity, and that it is not possible to increase the torque capacity per unit face width indefinitely by reducing the helix angle.
Small-Amplitude Vibrations of the Four-Bar Linkage Chain
Authors: Gayfer J. R. , Mills B.
Published: February 2007

Experimental and theoretical work is described dealing with the small-amplitude dynamic characteristics of plane four-bar linkages with prismatical links, one link being fixed in space. The object is to devise methods by which a design can be investigated as a vibrating system, given that it is already kinematically suited to its task.

The theoretical work is based on the assumption that only flexural vibrations are important, and uses the method of receptances to establish frequency equations which are then solved numerically to compare with the experimental results. The fundamental natural frequencies of the linkage were studied by free vibration tests and fundamental resonant response curves were obtained under conditions of forcing. The input was a mechanical scotch yoke drive when the links were flexible and an electro-magnetic exciter when the links were rigid.

Comparison of experiment and theory shows extremely good agreement for natural frequencies over wide ranges of configuration and acceptable agreement for the forced response curves.
Cross-Section Deformation Effects in the Vibration of Thin-Walled Beams of Arc Section
Authors: Hasan S. A. , Barr A. D. S.
Published: February 2007

Differential equations describing the coupling of ordinary bending motion with cross-sectional distortion are obtained for thin-walled beams of circular-arc cross-section using Hamilton's principle. In deriving the theory the cross-sectional deformation is assumed to take the form of the characteristic functions of a curved beam of the shape of the section. The variation with wavelength of the frequency spectra which result from the coupling is obtained. Experimental results showing the effects of the variation of the parameters of the beam geometry on the natural frequencies are in reasonable agreement with the theory.
Bounds on the Rate of Energy Dissipation in Bodies Deforming by Secondary Creep
Authors: Hodgkins W. R.
Published: February 2007

The present paper extends previous methods of bounding the rate of energy dissipation in a body deforming under secondary creep according to a power law . By an appropriate definition of the ‘representative stress’, bounds for a material with an arbitrary value of n are expressed in terms of a postulated known solution to the identical stress loading problem for a material with a different value of n. The results are applied first to idealized materials where n is a constant, and then extended to a class of non-idealized materials where n is a monotonic increasing function of stress.
Small-Deflection Creep Buckling of Magnesium Alloy (Magnox AL80) at 295°C
Authors: Freed N. H. , Seyna F.
Published: February 2007

The results of creep buckling experiments at 295°C on magnesium alloy specimens of two different diameters were compared with deflection rates predicted from a simple theory proposed by Alexander (1). Agreement was found to be adequate for design purposes, and within the scatter of the material data. The effect of eccentricity was evaluated and it was shown to have a negligible effect on bowing rates.
Behaviour of a Cylindrical Shell Subject to a Static Couple
Authors: Hedges J. L. , Mills B. , Cole B. N.
Published: February 2007

The Rayleigh theory of inextensibility is used to predict the displacement behaviour of a thin-walled cylindrical shell subject to a static couple. The effect of the position of load application is investigated. Characteristic curves are presented for a series of load positions for constant shell dimensions, together with curves showing the effect of different shell sizes. Experimental verification of the theory is provided, tests being performed on a cylinder in which the loads are applied at the ends of a diameter. Satisfactory correlation was found between the experimental and theoretical results.
Chatter Analysis by the Method of D-Partition
Authors: Porter B.
Published: February 2007

Contributions intended for publication as Research Notes should be limited in length to 1000 words and two illustrations, and should be addressed to the Editor of Proceedings at the Institution Headquarters in London.
Shakedown Pressures for Flush Cylinder-Sphere Shell Intersections
Authors: Leckie F. A.
Published: February 2007

Lower bound estimates have been found of the shakedown pressure for a flush radial cylinder-sphere intersection. This has been achieved by applying Melan's theorem and making use of elastic solutions already in existence. Results are presented in compact graphical form.
Vibration of Thin Cylindrical Shells
Authors: Warburton G. B.
Published: February 2007

Starting from Flügge's three equations of motion for a uniform thin cylindrical shell, the paper gives a general solution, from which the dependence of natural frequencies on shell dimensions and mode number can be investigated for any end conditions. This solution requires the assumption of a natural frequency and the determination of the corresponding shell length for the prescribed end conditions. Numerical results are given for shells with clamped ends and for shells with free ends; the variation of frequency factor and of mode shape with dimensional and mode parameters is shown and the accuracy of approximate theories assessed.
General Performance Indices for the time and Frequency Response for the Free Motion of Linear Discrete Control Systems
Authors: Soliman J. I. , Al-Shaikh A.
Published: February 2007

A method for evaluating general performance indices for the time and frequency response for the free motion of a linear stationary discrete control system described by the matrix equation

is given. A matrix B is formed from the system matrix A. The transpose of the inverse of the matrix B and its powers is then used to evaluate the expressions and where is a quadratic algebraic form, Δ m is the mth forward difference, and r = 0, 1, 2, …. From these expressions performance indices for the time and frequency response were then determined.
Buffeting Excitation of Boiler Tube Vibration
Authors: Owen P. R.
Published: February 2007

The origin of the vibration generated within an extensive bank of tubes that run transverse to the direction of gas flow through a boiler shell and whose movement is small enough in amplitude to have no perceptible effect on the motion of the gas, is examined on the supposition that, sufficiently deep inside the bank, the flow is essentially turbulent and, except for a general drift through the bank, exhibits no regular feature. Conditions of this kind are thought to be appropriate to certain types of heat exchanger used in nuclear power stations and operating at large Reynolds numbers.

The source of vibration, either structural or gaseous, is associated with the randomly fluctuating forces imposed on the tubes by the turbulent eddies, and a simple argument is put forward to account approximately for the length scale of the most energetic of these eddies and consequently the frequency with which they encounter the tubes. It is further argued that the tubes are aerodynamically discriminating in their force response which is thereby narrowed spectrally and confined to the neighbourhood of the frequency corresponding to the energetic eddies. The subsequent structural or acoustic response is even more sharpened spectrally, owing to the small damping inherent in the system.

A relation between the dominant frequency of the force fluctuations, the gas velocity and the geometrical arrangement of the tubes, that emerges from the argument, agrees in form with published observations of the sound emission from boilers under resonant conditions. A disposable constant appearing in the relation is also satisfactorily predicted in order of magnitude.

The analysis applies to only one possible form of the vibration phenomenon; other forms, aero-elastic and vortex-excited, may appear under suitable conditions dependent upon Reynolds number, structural stiffness and damping.
Circumferential Creep Strain of Cylinders Subjected to Internal Pressure: A Comparison of the Theories of Johnson and Bailey
Authors: Larke E. C. , Parker R. J.
Published: February 2007

When considering the creep of cylinders subjected to internal pressure, the theory of Johnson et al. takes into account progressive changes of radial, circumferential and axial stress at any point in the wall thickness. This approach differs from that put forward by Bailey, who assumed that these stresses remained constant with time. The present paper summarizes an examination of both theories, with particular reference to outside and bore diameters, and presents simple equations which enable circumferential strain to be calculated without using the complex graphical integration procedure suggested by Johnson. Furthermore, it is demonstrated that these equations are mathematically identical with those derived by Bailey.
Frequency Response of an Electro-Hydraulic Vibrator with Inertial Load
Authors: Ashley C. , Mills B.
Published: February 2007

During the past few years systematic vibration testing has played an increasing part in the evaluation of mechanical devices. The electro-hydraulic vibrator, consisting of a valve-controlled hydraulic cylinder, is capable of high thrusts over a fairly wide range of frequency. This paper examines the theoretical behaviour of such a vibrator which is itself similar to a hydraulic positioning system. The cylinder equations are extended to include end leakages and the servo valve is examined both for transfer characteristics and the interdependence of flow and load. It is shown that the classical square root relationship between pressure drop and flow does not necessarily apply for a two-stage valve with a spring-centred second stage and that a dimensionless number known as the valve load compensation coefficient describes these characteristics. For practical valves it is possible for the flow to be almost independent of the load over a wide range of operating conditions and thus a linear transfer function can be used for the valve-cylinder combination. The experimental work shows good agreement between the theoretical characteristics and those found in practice.
Factors Affecting the Performance of the Supersonic Parallel Diffuser
Authors: Martin B. W.
Published: February 2007

Following the work of Baker and Martin (1), this paper provides further information about static pressure recovery in axi-symmetric supersonic parallel diffusers of fixed length and the same upstream generating nozzle when the diffuser cross-sectional area is varied over a wide range. Correlations based on these and associated experiments by Martin and Baker (2) indicate an area ratio for maximum possible static pressure recovery. At breakdown of the single shock, the diffuser stagnation pressure ratio corresponds to that for normal shock pressure recovery, while the outlet Mach number becomes independent of area ratio as the latter increases. The factors which influence the development and stability of the single shock regime are considered in some detail, from which the role of the boundary layer is shown to be predominant.
Note on Relationships between Friction and Liquid Cross-Sections during Two-Phase Flow
Authors: Chisholm D.
Published: February 2007

Relationships between the friction pressure gradient and the cross-section of the tube occupied by the liquid are developed for the flow of air-water mixtures in rough-walled horizontal tubes. The data indicate a pronounced change in the form of the relationships when the pressure gradient reaches a value of about 60 lb/ft2ft.
Machining Forces: Some Effects of Removing a Wavy Surface
Authors: Wallace P. W. , Andrew C.
Published: February 2007

Previous work has shown that during the removal of a surface waveform oscillating cutting force components arise which may have a phase difference with respect to the oscillating component of undeformed chip thickness; it has also shown that the shear angle is affected by the slopes of the surface waveform. However, no attempt to predict the oscillating force behaviour from the geometry of cutting has been reported. The present work attempts to achieve such a prediction by means of an analysis of the phase and magnitude of the oscillating force components acting in two directions; in the directions of the mean shear plane and of the tool rake face. In the analysis it is assumed that the shear angle oscillates in phase with and proportionally to the surface slope, and that the curvature of the chip varies with the undeformed chip thickness.

An experimental technique for cutting with variable undeformed chip thickness is described, together with a method for recording and measuring the oscillating components of force and undeformed chip thickness. Experimental results are presented which show the assumptions made in the analysis to be substantially valid; the predicted oscillating forces are shown to be in adequate agreement with experiment over a range of experimental conditions. It is shown that the oscillation of the shear angle is primarily dependent on the surface slope and that the frictional force behaviour is consistent with the characteristics of the two regions of friction, sticking and sliding, as found in work on cutting with constant undeformed chip thickness.
Design of Turbine Blades Suitable for Supersonic Relative Inlet Velocities and the Investigation of Their Performance in Cascades: Part II-Experiments, Results and Discussion
Authors: Colclough C. D.
Published: February 2007

This paper describes cascade tests which were initially done to see whether blades designed by conventional methods for subsonic flows would in fact accept supersonic velocities at inlet to the blades but it was found that they would not do so. An analytical method for the design of turbine blades to accept supersonic relative inlet velocities has been presented in Part I (1). A blade section was designed for isentropic flow and from tests run on a cascade of these, values for losses and allowable contraction ratios were obtained which were incorporated in a revised design method. The tests and results obtained from the first supersonic cascade are described and also the results from the modified design which was based on non-isentropic conditions.

The supersonic cascades were tested over a range of incidences in a small wind tunnel fitted with interchangeable liners to produce Mach numbers of approximately 1.5 and 1.3, Preliminary tests were also run at subsonic velocities. At design conditions flow-visualization by means of a Schlieren system showed wave formations in the blade passages which corresponded to the theoretical design values thus proving the validity of the design method. At off-design conditions a somewhat unusual shock-wave boundary-layer interaction was observed which appears to be associated with blades of this type. This was analysed by means of total head traverses, static pressure measurements and by the method of characteristics, and the effect which the configuration had on the downstream flow and losses is discussed.

Total head traverses were done at the exits from the blade passages and also downstream of the trailing edges and the velocity coefficients were deduced from these values and from static pressure measurements obtained from wall tappings. For the first cascade which had a flow turning angle of 128° the velocity coefficient was approximately 0.95 and for the last cascade which had a turning angle some 9° greater, the value was 0.94. These velocity coefficients are higher than those for subsonic blades at comparative turning angles.

With blades designed for supersonic flows by the method outlined in Part I (1) it appears to be possible to turn the flow through large angles such as 140° and to obtain acceptably high efficiencies. Tests in steam turbines indicate that with these blades the maximum efficiency is at least equal to that of a turbine designed for subsonic flow but that the heat drop is some 12 per cent higher.
Calculation of the Compression Index in Reciprocating Engines Using Gaseous Fuels
Authors: Annand W. J. D.
Published: February 2007

Some values of the compression index obtained by digital-computer integration of the first law of thermodynamics, with allowance for variable gas properties and for heat transfer between charge and walls, are first presented and discussed. These show the effects of some of the common fuel gases, and the changes produced by variations of engine geometry and running conditions. An approximate calculation method suitable for manual computation is also described.
Effects of Strain Rate and Temperature in Orthogonal Metal Cutting
Authors: Boothroyd G. , Bailey J. A.
Published: February 2007

A new theoretical analysis of the orthogonal cutting process is described which is based on the known behaviour of a single phase metal at high strains, strain rates and temperatures. The theoretical analysis applies to the case where a continuous chip is produced under non-lubricated conditions with the absence of a built-up edge on the tool face and indicates the important parameters in the cutting process. The theory is examined experimentally and its validity established. Finally, from a knowledge of the effects of strain rate and temperature on the yield stress of a single phase metal, the theory is used to predict the effects of changes in cutting speed and tool rake angle on the tool forces and geometry of the cutting process. These predictions are compared qualitatively with the results of cutting tests.
Observations of the Effect of Creep Relaxation on High-Strain Fatigue
Authors: Edmunds H. G. , White D. J.
Published: February 2007

Results are presented of high-strain endurance tests on 2‡ per cent chromium, 1 per cent molybdenum steel. As well as continuous cycling at room temperature and 600°C, the tests covered hold times of 30 minutes and 300 minutes at maximum strain at 600°C. For the shorter hold times, strain ranges extended down to less than ±0.1 per cent and for the longer hold times down to ±0.24 per cent.

In a few tests an attempt was made to modify the test environment in order to gain an indication whether corrosion effects are likely to be important in such tests.

It is argued that, for preliminary design purposes (pending the outcome of comprehensive endurance tests), extrapolation from high strains to low may be dangerous and that it may be preferable to use relatively simple creep data to gain an early indication of likely endurance properties with hold time. Such an interpretation is not inconsistent with the present or previously published data.
Experimental Investigation of the Behaviour beyond the Elastic Limit of Flush Nozzles in Cylindrical Pressure Vessels
Authors: Cottam W. J. , Gill S. S.
Published: February 2007

Eleven tests have been carried out on mild steel cylindrical pressure vessels with flush nozzles. The cylindrical vessel was 18-in outside diameter x 3/8-in thick and the nozzles covered a range of outside diameters from 2 1/2 in to 6 in and thicknesses from 1/8 in to 3/8 in. The nozzle-vessel weld was in all cases to B.S. 1500, Fig. 32 e.

Two plain cylindrical vessels 18-in o.d. x 3/8-in thick were also tested to establish datum curves for the vessels with nozzles.

Clock gauges and strain gauges capable of measuring up to 2 per cent strain were used to measure the strain and change of geometry in the vicinity of the nozzle-cylinder intersection. Measurements were also made of the pumped water volume as the pressure was increased.

After pressurizing until the main vessel had yielded the instrumentation was removed and all vessels were tested to rupture.

The results do not show a well defined plastic limit pressure as normally understood but it has been possible to define from the experiments a series of pressures for each specimen at which consistent patterns of stress, strain and deflection are evident. One of these pressures is chosen to derive an empirical relationship which can be used in formulating a minimum design requirement.
‘Suitable Mean Values’ in One-Dimensional Gas Dynamics
Authors: Livesey J. L. , Hugh T.
Published: February 2007

The problem of the definition of mean values of flow quantities for use in the application of one-dimensional gas dynamics to non-uniform flows is considered.

Previously given methods for this problem are surveyed and are shown to be considerably in error and to have some unsatisfying basis of definition. A more satisfactory basis is suggested, based upon enthalpy flux, and this is shown to be more general and to have a satisfactory thermodynamic basis, particularly in the definition of mean temperature.

The significance of the form of definition of mean total pressure in relation to the energy equivalent of the irreversibilities is stressed. ‘Availability or entropy flux’, ‘mass weighted’, ‘area weighted’, ‘mass derived’ and ‘momentum mixed’ definitions of mean total pressure are considered.

Data for typical velocity profiles, over a wide range of Mach number, and for all known methods of calculating mean values have been obtained and a graphical summary is presented here.

At first glance, the data would seem to indicate that the percentage error in calculating total pressure by the different definitions is small, but this is not so. To assess the errors introduced in estimating the irreversibilities of a length of duct by using mass derived or other definitions of mean total pressure, then the error should be estimated as a percentage of the relative differences of mean total pressure involved. The data list which the authors hope to publish separately and the graphs in this paper enable this to be achieved.
Some Preliminary Results for Conical Diffusers with high Subsonic entry mach Numbers
Authors: Livesey J. L. , Hugh T.
Published: February 2007

Some preliminary results are presented for the variation of total pressure loss coefficient with entry Mach number for conical diffusers. Included angles of 5, 8 and 12°, area ratios from 2 to 16 and entry lengths from 0 to 65 diameters are considered. In these initial tests the junction between the parallel entry pipe and the cone is sharp.

The variation of Mach number and total pressure loss in the entry pipe is predicted simply using measured friction factors and typical velocity profiles. These calculations give the entry conditions to the diffusers in the absence of the diffusers. The effect of the junction of entry pipe and diffuser on the entry pipe flow is thus correctly attributed to the diffuser in the assessment of its total pressure loss. In addition a correctly specified mean entry Mach number is obtained. These considerations enable the losses in diffuser-pipe conjunctions of high Mach number to be logically analysed from separate pipe flow and diffuser data.

The results obtained are unusual and indicate that previous assessments of diffuser performance at high Mach numbers have been confused by incorrect consideration of the effect of the diffuser entry pipe conjunction and incorrect specification of the effective mean entry Mach number. It is concluded that further experimental results are needed for developing compressible flows in constant area ducts in order that the present preliminary results may be made more precise. The momentum equation analysis in terms of suitable mean values is presented briefly.

Previous diffuser results for low subsonic entry Mach numbers are considered briefly in comparison. Serious errors are shown to be present in these early results. Typically the errors originate in the definition of loss coefficient and static pressure efficiency and the use of the mass derived mean concept. In some cases the quoted static pressure efficiencies imply a decrease in entropy for the diffuser flow at low area ratios.
Application of Variable Coefficient of Friction and Wear to Block Brakes and Clutches
Authors: Heap J. C.
Published: February 2007

A mathematical analysis correlates the coefficient of friction and the wear rate in terms of pressure, velocity, area, temperature, and so forth, over discrete experimental data ranges. The basic equations of total torque, total radial force, total tangential friction force, and ideal pivot for block brakes and clutches having the coefficient of friction initially a function of normal pressure and relative rubbing velocity have been developed for dry or slightly lubricated surfaces. Three conditions are analysed: uniform wear having the coefficient of friction a function of pressure and velocity, uniform wear having the coefficient of friction a function of velocity and mean pressure, and uniform pressure having the coefficient of friction a function of velocity.
Whirling of Shafts with Asymmetric Stiffness
Authors: Bones J. A. , Hannam R. G.
Published: February 2007

The whirling of a shaft with asymmetric stiffness and viscous external damping and with its mass concentrated at a point has been investigated. General solutions for the transient and forced whirls are given and are illustrated by records obtained from an analogue computer simulation of the shaft. Also experiments have been carried out on a test shaft with special arrangements for the control of damping and for the excitation of forced whirls.

The region of instability, the forms of the transient whirls, and the forced whirls produced by out-of-balance force have all been examined in detail.

In addition, it is shown that as the rotational frequency of an asymmetrically stiff shaft increases above the upper limit of instability its whirl behaviour tends towards that of a symmetrically stiff shaft.
Compressible Flow through Square-Edged Orifices: An Empirical Approximation for Computer Calculations
Authors: Annand W. J. D.
Published: February 2007

Contributions intended for publication as Research Notes should be limited in length to 1000 words and two illustrations, and should be addressed to the Editor of Proceedings at the Institution Headquarters in London.
Currentmeter Errors under Pulsating flow Conditions
Authors: Jepson P.
Published: February 2007

The paper deals with the effect of unsteady flow on the velocity registration of current-meters. In the first section of the paper, experiments are described which show that axial flow pulsations cause currentmeters to over-estimate and that flow fluctuations transverse to the mean velocity generally cause under-registration by amounts depending on the flow and meter parameters. From these tests general comments are made concerning the choice of metering station and to a lesser extent meter design. The second section is theoretical and deals with the effects of axially pulsating flows. It has been possible, using simple aerodynamic principles, to show how the meter design can be improved to minimize registration errors. The agreement between this theoretical approach and the registration errors obtained from experiment is fair.
Energy Dissipation at Plane Surfaces in Contact
Authors: Earles S. W. E. , Philpot M. G.
Published: February 2007

Experiments are described in which the frictional damping occurring at plane stainless steel contacts under oscillating tangential loads was measured for different periods up to a maximum of 5 times 106 cycles. Expressions for the damping under partial slip and gross slip conditions are derived using the Panovko-type approach and compared with experimental results. Close agreement is obtained for the partial slip region and fair agreement in the gross slip region. Discrepancies are traceable to variations in the experimental coefficient of friction. The variations of energy dissipation and coefficient of friction under constant normal load conditions and the development of surface damage are described and discussed. The nature of the damage has a major influence on the friction and thus on the damping. The fretting damage appeared to consist of flattened areas, inclined at a slight angle to the plane of contact, interspersed with pits. Loose oxidized debris had accumulated in the pits and because of its low resistance to sliding, caused a fall in the overall coefficient of friction. The resistance of the debris was found to vary with the applied load conditions.
Bounds for the Natural Frequencies of a Simply Supported beam Carrying a Uniformly Distributed Axial Load
Authors: Fauconneau G. , Laird W. M.
Published: February 2007

Upper and lower bounds for the eigenvalues of uniform simply supported beams carrying uniformly distributed axial load and constant end load are obtained. The upper bounds were calculated by the Rayleigh-Ritz method, and the lower bounds by a method due to Bazley and Fox. Some results are given in terms of two loading parameters. In most cases the gap between the bounds over their average is less than 1 per cent, except for values of the loading parameters corresponding to the beam near buckling. The results are compared with the eigenvalues of the same beam carrying half of the distributed load lumped at each end. The errors made in the lumping process are very large when the distributed load and the end load are of opposite signs. The results also indicate that the Rayleigh-Ritz upper bounds computed with the eigenfunctions of the unloaded beam as co-ordinate functions are quite accurate.
Inertia Forces in a Four-Bar Linkage
Authors: Smith M. R. , Maunder L.
Published: February 2007

A method of determining the inertia effects in a four-bar linkage is described. General expressions are derived for the forces acting at the joints of the mechanism, and their variations with crank angle are shown graphically in some illustrative examples. The effects of balancing and of changes in the mass parameters of the linkage are discussed.
Effect of a Tensile mean Stress on the Alternating Stress Required to Propagate An Edge Crack in Mild Steel
Authors: Frost N. E. , Greenan A. F.
Published: February 2007

The conditions governing growth or dormancy of fatigue cracks in mild steel subjected to the general tensile loading cycle σm± σa, where σm ≥ σa, have been studied using plate specimens containing two small opposite co-planar edge cracks. It was found that, as in the case of zero mean load, these conditions were defined by the value of the parameter σa3 l; if σa3 l ≥ Cm a crack would grow, whereas if σa3 l < Cm it would remain dormant, where Cm depended on the value of the ratio σm/σa. Its value at σm/σa = 1 corresponded to that derived from the zero mean load value by assuming that the loading cycles ± σa and 0 to σa were equivalent. The value of Cm then decreased linearly as the ratio σm/σa increased to 3, after which it remained constant as σm/σa increased further, provided that the applied loading cycle did not result in the bulk of the specimen deforming plastically. This lower limiting value was found to correspond to that predicted from the known growth rate of a crack in mild steel, assuming that a crack cannot grow at a rate less than one atomic spacing per stress cycle.
Power-Speed Characteristics of Differential Transmissions
Authors: White G.
Published: February 2007

An index number is proposed as a means of describing the torque-speed characteristic of a variable-ratio unit. This index number is combined with conventional relations describing a differential gear in order to deduce the limiting power-speed envelopes of a differential transmission.

Input-coupled and output-coupled differential transmission systems are examined and shown to have markedly different characteristics; for this reason they cannot be considered inversions. It is evident that the general relations describing each type of transmission can be used to synthesize a transmission or to analyse an existing transmission.
Blade Loadings for Hovercraft and other Radial Flow Fans
Authors: Carter A. D. S.
Published: February 2007

The layout of a hovercraft leads naturally to the choice of a radial outward flow fan, but the aerodynamic requirements are more stringent than those normally associated with industrial fans. In this paper a blade loading criterion used extensively in axial flow compressor practice has been adapted to the more general case of radial flow fans. Using this criterion maximum fluid deflections and maximum temperature rise coefficients have been calculated. It is shown that fluid deflections in radial fans should be substantially lower than those in axial flow machines. For high work output the ratio of rotor outside diameter to rotor inside diameter should be as close to unity as is mechanically possible. Inlet guide vanes would be of no benefit to the conventional industrial type centrifugal fan, but for such applications as hovercraft inlet guide vanes could be most beneficial.

The paper outlines those areas in which further research is necessary fully to confirm the approach, and hence the quantitative values, given in this paper.
Vibration of Box-Type Structures
Authors: Dickinson S. M. , Warburton G. B.
Published: February 2007

The free flexural vibrations of open and closed rectangular boxes are considered; a theoretical solution using a sine series is presented. Natural frequencies and nodal patterns obtained using this analysis are compared with experimental results and the practical usefulness of the analysis is assessed. Although the assumed mathematical models are not true representations of the practical systems, the agreement achieved between theoretical and experimental results is shown to be good.
Plastics Sandwich Beams under Bending Loads of Short Duration
Authors: Ogorkiewicz R. M. , Sayigh A. A. M.
Published: February 2007

Design of plastics sandwich structures calls for methods of predicting their deformation under load, which were studied with particular reference to beams under three- and four-point bending and under uniformly distributed loads. A preliminary series of tests established the stress-strain characteristics of p.v.c. (polyvinyl chloride) and polyurethane core and rigid p.v.c. skin materials. Using stress function solutions deflections and skin strains of different beams of these materials were then calculated and compared with experimental results obtained with beams made of the same combinations of materials. Good agreement was found for loads of short duration within the limits imposed by local stress concentrations.
Mechanical Properties of Some Cold-Rolled Plastics
Authors: Williams J. G. , Ford Hugh
Published: February 2007

A technique for cold rolling thermoplastics is described and the results of compression tests on some rolled materials are described in terms of basic stress-strain curves. There is evidence of a general improvement in mechananical performance particularly for biaxially oriented (cross-rolled) material. Density changes are examined and a pronounced resistance to environmental cracking for cold-worked materials is reported.
Link-Mounted Gear Trains
Authors: Merritt H. E.
Published: February 2007

This paper distinguishes, as a subject worthy of recognition and study in its own right, the class of mechanism comprising gears mounted with axes coincident with the pivot points of a linkage. The same concept serves for the analysis of the assembly conditions of multiple-contact gear trains, in which a ‘virtual’ linkage may be visualized.

A variety of known mechanisms, commonly dealt with, for design analysis purposes, on an ad hoc basis, fall within the same broad concept; no novelty is claimed for any mechanism as such, and the paper merely attempts to indicate some principal sub-divisions into which broader studies might be grouped. These fall under the two main categories of ‘kinematic’ and ‘geometrical’ analysis, although these again converge when a linked gear train is used to form a differential mechanism by which a function of the deformation of the linkage is superimposed on the angular motion of the gears and their connecting shafts.

It is possible that co-ordinated studies of linkages and gears in combination, as here adumbrated, might lead to the development of new, particular mechanisms capable of engineering application.
Optimization of Vibration Absorbers: Iterative Methods for use on Systems with Experimentally Determined Characteristics
Authors: Stone B. J. , Andrew C.
Published: February 2007

Methods are presented for the optimization of the design of an absorber, incorporating combined spring and damper elements of polymeric material, and coupled to a complex main system. These methods, which involve rapidly convergent iterative procedures, utilize directly the experimentally measured characteristics of both the absorber element material and the main system.

Butyl rubber is found to be a convenient and effective absorber element material, reducing the response of a model complex main system, with damping of a level typical of engineering structures, by a factor of approximately four.
Two-Node Mode Shape and Frequency Parameter of Torsional Oscillations in Engines
Authors: Gupta K. N.
Published: February 2007

An attempt is made to evolve some charts which should directly read the two-node frequency parameter and mode shape of engine systems having four to eight cylinders with equal moments of inertia per cylinder line and equal shaft stiffnesses between the cylinder centres. The dynamic matrices for these systems are iterated upon in a digital computer to obtain the two-node frequency parameter for different ratios of inertia per cylinder line to flywheel inertia and crankthrow stiffness to stiffness of shaft between last cylinder and flywheel. The value of the frequency parameter is further used to evaluate relative amplitudes. The results indicated by the charts are in close agreement with the exact values.
Experimental Determination of the Complete Dynamical Properties of a Two-Degree-Of-Freedom Model Having Nearly Coincident Natural Frequencies
Authors: Traill-Nash R. W. , Long G. , Bailey C. M.
Published: February 2007

Existing techniques of resonance testing have shown a marked inability to find the principal modes, natural frequencies and levels of damping in a structure which possesses two or more close natural frequencies (1)§.

This paper describes an experimental investigation on a two-degree-of-freedom model of a technique which makes use of dynamical influence coefficients (or receptances) measured at a number of stations on the structure (2) (3) (4) (5). The measured coefficients are used to calculate natural frequencies and modes of vibration, and the mass, damping and stiffness properties of the system. Several model configurations having different natural frequency separations were tested and no special difficulty resulted when natural frequencies were close or even coincident.
Interaction of a Whirling Rotor with a Vibrating Stator across a Clearance Annulus
Authors: Black H. F.
Published: February 2007

Where a rotor runs within a clearance space, the clearance being comparable with rotor mass unbalance, the synchronous whirling behaviour of the rotor may be considerably affected by intermittent interaction with the stator at the clearance position. Discontinuity and jump phenomena may occur: in general, behaviour will be different with increasing speed from that with decreasing speed, and in either case zones may exist in which rotor-stator interaction is possible but not certain. In the analysis here presented, rotor and stator are regarded as linear multi-degree-of-freedom systems including damping; dry friction at the clearance space is taken into account. Discussion is limited to cases with radial symmetry, and interaction is assumed limited to the position of the clearance space. Polar receptances are used to establish equilibrium conditions with interaction, and speed zones are defined within which interaction may occur. Some hypothetical cases are fully explored, demonstrating that rotor-stator interactions may occur in a variety of forms and circumstances.

Interactions with dry friction counterwhirling are also considered. Some experimental results on counterwhirl within a ball bearing are given and qualitatively compared with theory.
Creep Recovery of Commercially Pure Copper
Authors: Henderson J. , Snedden J. D.
Published: February 2007

Tension and torsion creep recovery tests on commercially pure copper at 150, 200 and 250°C are reported. Recoverable strain can range from a negligible percentage to approaching 100 per cent of the total creep strain developed, depending on stress, creep period preceding unloading, and current recovery time. An empirical equation relating creep recovery to these characteristics of the initial creep test is given.
Creep of a Carbon-Manganese Steel under Cyclic Stress and Temperature Conditions
Authors: Day M. F. , Cummings W. M.
Published: February 2007

Nearly all creep data are obtained under closely controlled constant conditions of load and temperature. Most high-temperature plant, however, is subject to cyclic variations of both, due to periodic off load or reduced load conditions.

Test data for a C-Mn steel are presented for various cycles of stress and/or temperature. The effects of cycling of stress or temperature, and of in-phase changes of both, are predictable within reasonable limits. It is shown, however, that with out-of-phase changes in stress and temperature, i.e. high stress/low temperature to low stress/high temperature conditions, a very rapid acceleration of strain can occur.
Evaporating Fluid Flow in Pipes: A Theory for the Prediction of Phase Velocity, Pressure Drop and Critical Outlet Conditions for Evaporating Annular Flow in Pipes
Authors: Linning D. L. , Pexton A. F. , Alderson M. A. H. G.
Published: February 2007

The theory of evaporating flow given in this paper is believed to be an advance on what has hitherto been available in that it makes due allowance for the effect of vapour condensation which occurs simultaneously with vapour expansion. The basic theory is applicable without modification to any fluid undergoing evaporating flow in the annular mode, given suitable correlations for wall and interphase friction factors as defined in the paper. Preliminary correlations, which can only be very rough, are provided for water. A lot of experimental work on a variety of fluids would be required to achieve a position from which general correlations could be developed. The theory incidentally permits prediction of critical outlet conditions and some interesting comparisons with available experimental data have been made.
Transverse Vibration of a Class of Non-Uniform Beams
Authors: Sanger D. J.
Published: February 2007

The free and forced transverse vibrations of a class of non-uniform beams, which includes as special cases the wedge and cone, are considered. Receptances, frequency equations, mode shapes and natural frequencies are presented for simple end conditions.
Numerical Solutions of Viscous Flow through a Pipe Orifice at Low Reynolds Numbers
Authors: Mills R. D.
Published: February 2007

Numerical solutions of the Navier-Stokes equations have been obtained in the low range of Reynolds numbers for steady, axially symmetric, viscous, incompressible fluid flow through an orifice in a circular pipe with a fixed orifice/pipe diameter ratio. Streamline patterns and vorticity contours are presented as functions of Reynolds number. The theoretically determined discharge coefficients are in good agreement with experimental results of Johansen (2).
One-Way Buckling of a Compressed Strip under Lateral Loading
Authors: Allan T.
Published: February 2007

This paper is concerned with the problem of the buckling of a long thin strip column rigidly supported along its length on one side, and subjected to a uniformly distributed force on the other. It is shown that the mode of buckling failure of the strip column under these conditions is independent of its length and always occurs with the sudden formation of a single buckle. The critical load also is independent of the column length although the post-buckling load is a function of the length. It is evident that the magnitude of the critical load is profoundly influenced by the degree of initial deflection or imperfection present in the column.

An analysis of the problem is given together with experimental verification. The effect of the testing machine characteristics is also examined.

The particular case of strip column buckling considered here is of vital importance to the solution of a number of plate and shell buckling problems, and sheds new light on these. A further paper on this extension of the theory is in preparation.
Experimental and Analytical Investigation of the Behaviour of Cylindrical Tubes Subject to Axial Compressive Forces
Authors: Allan T.
Published: February 2007

This paper describes experimental work which was undertaken to investigate the buckling characteristics of axially loaded cylindrical tubes and presents a theoretical basis for analysing tube behaviour.

This is a radical departure from the existing theories in the literature which are not supported by experimental evidence. It is shown here that the tube failure is a ‘one-way’ buckling phenomenon where buckles can appear singly or in sequence. Two basic failure modes are established. One is due to an outward movement of the tube wall which produces a ripple or bellows formation and is fundamentally a yielding phenomenon. The other is inward movement which produces diamond shaped indentations and is an elastic failure. Mainly in the latter case, the small deviations from the true cylindrical form are the critical elements in determining the value of the failure load.
A Carnot Theorem for Split Torque Variable Speed Gears
Authors: French M. J.
Published: February 2007

Used in conjunction with differentials a continuously variable gear can vary a larger power through a smaller range of ratios: limits on this process are established.
Displacement Bounds for Dynamically Loaded Elastic Structures
Authors: Martin J. B.
Published: February 2007

A technique for determining upper bounds on displacements at chosen points of certain dynamically loaded elastic structures is presented. The technique is an extension of earlier work (1), and makes use of the classical potential energy theorem for structures in which displacements are small. In certain cases the method can be extended to finite displacements by involving a stability requirement. An example involving impulsive loading is given.
Flexural Vibration of Symmetrical Multi-Layer Beams with Viscoelastic Damping
Authors: Agbasiere J. A. , Grootenhuis P.
Published: February 2007

The flexural vibrations of beams can be reduced by introducing sandwiched layers of energy-dissipating materials. The equations of motion are derived for flexural vibrations of symmetrical, multi-layer sandwich beams. Two types of beams are considered, depending on whether the central layer is energy dissipating when the number of layers will be n = 4 i − 1, where i = 1, 2,…, or whether the material of the central layer is perfectly elastic when n = 4 i + 1. The total number of equations of motion will be i + 1 for each type. These equations will be non-linear when the properties of the energy-dissipating materials are strain dependent. A numerical method of solution has been introduced by transforming the equations of motion into sets of non-dimensional simultaneous equations and using finite difference methods. The simplest type of beam has three layers but even this leads to a set of four simultaneous equations of the twelfth order.

It is shown as an example that the strain dependence of a typical viscoelastic material has only a second order effect upon the computed response. Experimentally determined values of frequency, phase angle and mode shapes under conditions of steady state are compared with computed data and the agreements are such that the response to excitation in flexural motion of symmetrical, multi-layer damped beams can now be calculated with confidence even for the lower modes.