bluuebunny/crossref_metadata_2025 huggingface dataset:
Programming for Electronic Computation of Stresses in Piping Systems
Authors: Coldham V.
Published: February 2007

Details are given of methods of calculation of thermal stresses and deflections in complex piping systems, suitable for use with a digital electronic computer. A résumé of a working computer programme for multi-branch unconstrained systems is made, and a six-anchor three dimensional example solved automatically by this programme is described.

Extension of matrix analysis for the more complicated constrained and looped layouts is developed in Appendix I, where a method of interconnecting solutions of subsystems to give solutions of piping structures of very great complexity, is outlined.
Study of the Symmetrical Elastic Loading of Some Shells of Revolution, with Special Reference to Toroidal Elements
Authors: Turner C. E.
Published: February 2007

The governing equations for the elastic behaviour of axisymmetrically loaded thin elastic shells of revolution are derived and applied particularly to toroidal shells where the radius of revolution is much larger than the radius of ring cross-section. It is shown that under these conditions the approximate equations are a special case of the Mathieu type. Some solutions have recently been tabulated enabling the theory to be applied to structures such as toroidal pressure-vessel heads, expansion bellows and similar shapes. Comparison is made with an approximate series solution of the same equations.
Photo-Elastic Exploration of the Stresses in a Design for a Full-Bore Closure for a Reactor Pressure Vessel
Authors: Snell C. , Jessop H. T.
Published: February 2007

This paper describes the analysis, by photo–elastic methods, of a model of a design for a full-bore closure for a reactor pressure vessel.
Study of the Clamping Conditions in a Connecting-Rod Big End
Authors: Lambert T. H.
Published: February 2007

The connecting rods of most reciprocating engines are required to carry a direct tensile load at some time during the engine cycle. This load is transmitted by the big-end bearing-cap bolts and produces in these members incremental direct and bending stresses, which are dependent on the stiffness of the big-end bearing-cap. The problem is statically indeterminate but can be solved by using the compatibility condition. Expressions for the direct and bending stresses are given, and these are compared with measurements made with electrical resistance strain gauges.
Vibrations of Rotating Cantilever Blading: Theoretical Approaches to the Frequency Problem Based on Energy Methods
Authors: Carnegie William
Published: February 2007

A theoretical expression is obtained for the work done due to centrifugal effects when a rotating cantilever blade executes small vibrations. The total potential energy and kinetic energy of the system are formulated, use being made of previously derived expressions for the stationary blade.

By use of Rayleigh's method an equation for the fundamental frequency of vibration is established and, for the case of a straight blade of uniform and symmetrical cross-section, a solution is deduced based on an approximate shape for the normal elastic curve. The characteristic differential equations of motion for the rotating system are obtained from the energy expressions by use of variational calculus. Coriolis effects, being small, can be neglected in the analyses.
Elastic Interactions at the Junction of an Assembly of Axi-Symmetric Shells
Authors: Zaremba W. A.
Published: February 2007

Based on certain limiting assumptions a general solution in matrix form is given for the self-equilibrated loads caused by discontinuity at the junction of axi-symmetric shells.

Formulae and computation forms are given for the practical derivation of quantities defining local bending of cylindrical, spherical and conical shells and the components of their membrane displacements under several standard types of loading.

Derivation of some formulae is indicated and a numerical example illustrating the use of the method is included.

In the discussion this particular ‘computation procedure’ approach to calculation of shells is compared with ‘explicit formula’ approach and the influence of normally neglected membrane rotations is assessed.
Mixing of Coaxial Streams inside a Closed Conduit
Authors: Mikhail Sami
Published: February 2007

In this paper the linearized integral equations of motion are used to solve the problem of turbulent mixing of two coaxial streams inside a closed conduit.

Similar to the problem of mixing of unbounded coaxial streams, the problem is too complicated to be solved by the equations of motion, but by specifying a shape for the velocity distribution across the streams at all normal sections, the solution has been simplified. For every region of the mixing regions, the radius of the core, the external radius of the inside stream and the velocity on the axis are determined by the integral equations of motion. The solutions are then joined by making the velocity and radius continuous at the transition sections. In this way a complete picture of the flow pattern is obtained.

In order to test experimentally the formulated theory, the paper describes experimental data from a coaxial air to air jet-pump having a mixing chamber of constant diameter. The data consist of complete velocity traverses and wall static pressures taken at different flow ratios. The primary and secondary streams were of the same density, incompressible, subsonic and isothermal.

The main conclusion from the experiments is that the theory gives an overall picture of the mixing process which is in the main correct, though it might be inaccurate in some of the details.
Application of Macaulay's Method to Vibrating Beams
Authors: Black H. F.
Published: February 2007

Complete non-series solutions for steady-state vibrations of uniform-section beams with all possible combinations of various supports are given, using a generalization of the Macaulay notation commonly used for evaluating static beam deflections. The presence of flexible restraints and elastic hinges is considered within the same framework. The application of the method is shown by some specific calculations.
Use of Excess Constraints in Structural Analysis
Authors: Plunkett R. , Gurtin M. E.
Published: February 2007

This paper describes a method of structural analysis whereby extra constraints are applied to the structure to keep the effects of any applied forces within a part of the structure so small that it may be readily analysed. For the constrained structure, one computes the stiffness matrix by imposing the simple unit motions called for and calculating the forces at the constraints. A judicious choice of constraints makes the calculation of the elements of the stiffness matrix easy and may make most of them zero. The excess reactions may then be removed by a partitioning and partial inversion process.
Making of Thin Metal Shells for Model Stress Analysis
Authors: Thompson J. M. T.
Published: February 2007

A method is outlined for the manufacture of small thin metal shells. Details are given of the production of a spherical copper shell of diameter 6 in., and wall-thickness 0·004 in. The shell is deposited electrolytically on a wax surface of the appropriate shape, and the wax is subsequently melted away. Arrangements of anode and cathode in the electrolysis process are examined for uniform thickness of metal deposit on surfaces of various shapes.
Behaviour of Perforated Plates under Plane Stress
Authors: Bailey R. , Hicks R.
Published: February 2007

A theoretical method is developed for determining the elastic behaviour of end-loaded plates completely perforated with closely spaced circular holes forming a square or diagonal pattern. The general method of solution has been verified by experimental work for particular types of loading. The following problems are considered in detail: (1) Unequal uniform applied extensions in the × and y directions; (2) Uniform applied shear. Using a digital computer, complete solutions have been obtained for the stress distribution in plates with holes having pitch to diameter ratios of 1·2, 1·4, 1·7, 2·0, and 3·0, respectively. These solutions have been used to obtain design curves for (1) effective Young's modulus; (2) effective shear modulus; (3) effective Poisson's ratio; (4) variation of applied load; (5) variation of stress across ligaments; (6) stress concentration factors. For plates with a square or diagonal system of holes, the above curves are sufficiently extensive to be applicable to all problems likely to occur in practice.
The Effect of Material Properties on the Lubrication of Elastic Rollers
Authors: Dowson D. , Higginson G. R.
Published: February 2007

The effect of the significant variables on solutions to the problem of isothermal lubrication of elastic rollers is examined. It is found that for realistic materials, speeds, and loads, the outlet pressure peak predicted by Grubin (4) is always present. The magnitude of this pressure peak may exceed the maximum Hertzian pressure. It varies only slightly with load, but markedly with speed and materials. The influence of these variables on the shape of the outlet pressure curve explains the difference between Petrusevich's results (5) and those presented earlier by the authors. The stress concentrations produced near the surface by the outlet pressure peak would have a significant effect on the fatigue life of rolling elements.

It is found that the centre-line film thickness varies hardly at all with load, significantly with material properties and considerably with the product of speed and inlet viscosity.

Pressure distributions and film shapes are presented for five cases to illustrate the influence of load, speed, and materials. In addition, maximum principal stress differences are shown for two solutions.
Theoretical Aspects of the Roots Air Motor
Authors: Patterson J.
Published: February 2007

The following analyses constitute a preliminary attempt to provide a sound theoretical basis for future work to be carried out on Roots motors and blowers, the former only being considered in the present paper.

An ideal motor is defined, thereby facilitating the analyses and setting a standard of performance for the conventional motor operating on the non-expansive cycle. The low absolute thermodynamic efficiency of the ideal being a direct consequence of non-expansive working, a standard of performance for expansive working is set by the definition of a perfect motor.

It is shown that ideal motor torque is reduced as the number of rotor lobes increases, and that severe alternating torques, which are largely tied up with the motor mean torque, occur in the rotors themselves.

In the real motor, deviations from the ideal are due to a number of separate causes. A quasi-analytical solution has been obtained for the adverse torque due to subsonic discharge, whilst a pair of simultaneous differential equations permits an estimate of the adverse torque due to pressure variations between the rotors.

The results obtained suggest a number of design changes in the conventional Roots motor.
Temperatures Reached in Friction Clutch Transmissions
Authors: Newcomb T. P.
Published: February 2007

Expressions are given to determine the torque capacity of a clutch and the rate at which heat is dissipated by dry friction during a single clutch engagement, together with equations to enable calculation of the rubbing-path temperatures as well as temperatures at various depths inside the contacting bodies during the slipping period. It is shown how the maximum friction surface temperature varies with the thickness of the pressure plate and for design purposes a rapid method of calculating temperatures is given when the slipping time is known. Some curves showing the agreement between temperatures determined theoretically and measured experimentally inside a clutch facing during continuous slipping are given.

The temperatures attained after regular repeated clutch engagements are considered when cooling is by convection alone and a method of calculation is outlined, when in addition to convection losses radiation losses need to be taken into account. A formula is given to enable the area of the rubbing path to be calculated if the temperature is not to exceed a specified value.

In an appendix the temperatures are calculated when the torque linearly decreases with slipping speed and a comparison is made with the case when the torques are assumed to be constant.
Viscosity of Steam at Supercritical Pressures
Authors: Whitelaw J. H.
Published: February 2007

This paper records the measurement of the kinematic viscosity of steam at pressures from 200 kg/cm2 to 800 kg/cm2 and at temperatures from 370°C to 650°C. The Rankine-type viscometer used for these determinations was originally designed by Kjelland-Fosterud, who obtained preliminary results from it. To improve the reliability and precision of results, several modifications to the original apparatus have been effected and these are described in the text. The standard deviation of the measured values is ± 1.5 per cent and, in general, these are lower than the accepted values given by Timrot. Further, the results indicate a smaller dependence on pressure than hitherto accepted.
Chatter Patterns Formed on the Surface of Thin Cylindrical Tubes during Machining
Authors: Arnold Ronald N.
Published: February 2007

The patterns formed on the surface of thin cylinders during machining are shown to result from self-induced and forced vibration. As metal is removed, the natural frequency of the cylinder slowly decreases, thus decreasing the number of surface waves accommodated around the circumference. The pattern repeats itself each time the number of surface waves per revolution is decreased by one. The slow rise and fall of vibration intensity depends in the main on the interaction of part of the cutting tool with the surface waves cut during the previous revolution.
Large Strains of Drum Heads Studied with Silicone Rubber Models
Authors: Fessler H. , Foreman J. J.
Published: February 2007

A technique for producing accurate models is described. The models were subjected to internal pressure and the displacements of points on the outer surface were measured with a travelling microscope. From these measurements the radii of curvature and the rotation of the elements were determined graphically and the bending moments calculated.

The greatest bending moments were found to be proportional to the percentage increase in head height and almost independent of Poisson's ratio of the material except for the change in flexural rigidity. The effect of large strains on the bending moments in any drum head can therefore be calculated if the relation between increase in head height and pressure has been determined and the bending moments for one pressure are known.
The Inverse Problem with Sinusoidal Forcing of Linear Second-Order Systems
Authors: Ury J. F.
Published: February 2007

Different methods, in part known from the literature, are reviewed, by which the inverse problem with sinusoidal forcing of linear second-order systems can be solved. Various geometrical relations are explained which may be used in plotting response curves with greater ease, speed, and accuracy. If response analysis has to be based on measurements of magnitude alone, integration of the magnitude versus frequency curve appears to form a convenient and accurate means. The limitations of an analysis based on magnitude curves alone are discussed.
Linear Theory of Non-Uniform Torsion
Authors: McMinn S. J.
Published: February 2007

St. Venant's solution of the torsion problem applies only to cases where the cross-sections all warp in the same manner and by the same amount. This paper gives the solution for the cases where warping varies, either because there is a cross-section where there is a restraint on deformation or because the applied torque varies along the bar. The solution is restricted to small deflections such that the principle of superposition may be applied.
On the Ratio of Transverse to Axial Strain and other Tensile Properties of a Cold-Rolled Steel Alloy
Authors: Shelton A.
Published: February 2007

Tensile tests have been performed on a 0.4 per cent carbon steel alloy in order to determine the behaviour of the lateral/longitudinal strain ratio. The material was cold rolled to produce a number of sheets covering the range 0–80 per cent reduction and test-pieces were prepared from strips cut from these sheets at each 15° between 0° and 90° to the rolling direction.

The results are presented in graphical form and show the relationship between true tensile stress versus rolling reduction and the corresponding point-by-point equivalent contraction ratio versus rolling reduction. The experimental contraction ratio curve was computed from the strains in two transverse directions and represents the uniform contractions which would be experienced by an isotropic bar. This curve is compared with a theoretical curve which is based on the assumption that a metal flows without change in its permanent volume. The influence of cold rolling on some of the mechanical properties of these metals is also shown.

It is concluded that provided accurate values of the elastic constants are known, the equivalent isotropic contraction ratio for a given tensile strain may readily be computed. The results show that very small permanent volume changes occur but that it is impossible to obtain absolute values by this method. It is also concluded that large errors can arise in stress analysis problems if the variation in the elastic ‘constants' with cold work is ignored.
Theoretical Study of Tube Sinking through Conical Dies
Authors: Moore G. G. , Wallace J. F.
Published: February 2007

A study has been made of sinking of a tube, of a non-strain-hardening material, through a smooth conical die without any limitations on the diameter to wall thickness ratios, and instantaneous stresses and strains have been determined. It is shown that this theory gives similar values of external forces to a simpler stress solution based on mean tube radii. The equality has enabled coulomb friction and strain hardening to be included in an analysis of stresses and strains and has enabled drawing loads and thickness changes to be determined.

Computations for the theories show the influence of the wall thickness to diameter ratio, friction and strain hardening.
Elastic Stresses Due to An Interference Fit Pin in a Rectangular Plate of Finite Width
Authors: Lambert T. H.
Published: February 2007

The stress distribution in a rectangular plate of finite width due to an interference fit pin, obtained from two dimensional photoelastic models, is compared with the stress distribution in a circular plate of outer diameter equal to the minor axis of the plate. For ratios of hole diameter to plate width ( D/W) of less than 0·6 it is shown that the Lamé theory for the circular plate sensibly predicts the principal stresses on the hole boundary of the rectangular plate. For higher values of D/W the Lamé equations underestimate the radial stress and over-estimate the hoop stress on the hole boundary, although the principal stress difference is predicted with reasonable accuracy up to D/W = 0·8.

The major discrepancy between the two distributions occurs at the edge of the plate, where the hoop (or tangential) stress for the rectangular plate is considerably higher than for the circular plate.

Finally the effect of end shape is discussed and it is shown that although the stress distribution across the transverse axis of the plate approximates more closely to the Lamé solution for square and circular ended plates, the maximum principal stress difference at the hole boundary no longer occurs at this section but moves round the hole boundary in the direction of the foreshortened end.
Effect of Sheet Thickness on the Rate of Growth of Fatigue Cracks in Mild Steel
Authors: Frost N. E. , Denton K.
Published: February 2007

Fatigue tests have been carried out on mild-steel specimens 10-in. wide by 0·3-in. and 1·0-in. thick. Each specimen contained a small central slit to initiate fatigue cracks and measurements of crack length were taken throughout the test. Comparison of the results with those obtained previously on 0·128-in. thick specimens (Frost and Dugdale (I)‡) showed that, for a given loading cycle and crack length, the rate of growth was independent of specimen thickness.
Temperatures Reached in Braking when the Thermal Properties of Drum or Disc Vary with Temperature
Authors: Evans D. J. , Newcomb T. P.
Published: February 2007

A numerical solution is given to the heat problem associated with braking when the thermal properties of a drum and disc vary with temperature.
Calculation of Surface Temperatures Reached in Clutches when the Torque Varies with Time
Authors: Newcomb T. P.
Published: February 2007

Equations are given which enable the slipping period, the energy dissipated and the temperatures reached at any instant during a single engagement of a clutch to be determined when its torque capacity is a function of time. Two typical torque-time variations are discussed and a comparison is made with the case when the torque is assumed to be constant.
Correlation of Various Types of Axisymmetric Overflows of Small Vorticity
Authors: Bunt E. A. , Kirk M. F.
Published: February 2007

Head and quantity observations of axisymmetric free overflow of water into straight-sided glass pipes were made during slow cyclic-flow transitions to observe the relation of head to discharge within the range of stable operating conditions for each of the various types of weir and orifice flow identified. These results have been combined with those of other investigators (on which this work has been based) to illustrate a correlation of the various coefficients of discharge in one or other of the following dimensionless forms:

in order to eliminate the effect of temperature, which is not always quoted. The relation of ‘critical’ flow ( NFr(h) = 1) to the various results for overflow is also shown.
Symmetric Bending of the General Shell of Revolution by Finite Difference Methods
Authors: Penny R. K.
Published: February 2007

This paper gives a theoretical method of analysis of the elastic bending of the general thin shell of revolution, subjected to axially symmetrical loading and temperature variations, by the use of finite differences. The method is comprehensive and applies when the shell thickness or material properties vary and could be used in a wide range of problems concerned with the design of pressure vessels and other shell structures.

To illustrate the application of the method five typical shell elemental shapes are analysed. Comparison with other theories, which are available for these cases, shows the finite difference approach to be highly accurate.
Operations Cycle of the Stirling Engine with Particular Reference to the Function of the Regenerator
Authors: Walker G.
Published: February 2007

The basic elements of a Stirling engine, the regenerator and the compression and expansion spaces may be arranged in three different ways. The preferred arrangement is the displacer-piston in a single-cylinder system. With a machine of this type, acting as a refrigerator, some experiments were carried out to determine the effect of the regenerator on the machine output. The experimental regenerators were made up of packs of wire gauze. Different sizes and arrangements of meshes were tried, and it was found that dense meshes with small diameter wires gave the best results. The theory of the operational cycle of a Stirling engine is not fully developed, but a simplified theory can be used to investigate the effects of some of the independent design parameters. A recent more complex theory promises to make possible a closer relation of the experimental and theoretical performance of an engine.

The operating conditions of a regenerator in a Stirling engine are different from those assumed in the existing theory of regenerators developed mainly for application to gas turbines. Even so values for the efficiency of the regenerator in a particular case can be estimated using the theory. The few values obtained confirm the conclusions of the experimental work.
A Bound Method for Creep Analysis of Structures: Direct Use of Solutions in Elasticity and Plasticity
Authors: Calladine C. R. , Drucker D. C.
Published: February 2007

A structure of given geometry is made of a material whose stress-strain rate law is of the form

where Bn and n are properties of the material. The authors set out to consider the effects on the load-rate of deflection characteristics of the structure of changes in the index n. A non-dimensional diagram is used to compare the load-rate of deflection characteristics of the structure for different values of n. A recent theorem is quoted which indicates that in this diagram the (closed) curves corresponding to different values of n nest inside each other as n increases. As the curves for n = 1 (which corresponds to linear elasticity) and n=∞ (which corresponds to perfect plasticity) may usually be established without much difficulty, they may therefore be used conveniently to locate the region in which the curves lie for any other intermediate value of n. Inspection of the curves for different values of n for several structures indicates that the theorem may become a useful tool in the study of the steady creep of structures or, by analogy, the study of non-linear elasticity.
Effect of Mean Stress on the Rate of Growth of Fatigue Cracks in Sheet Materials
Authors: Frost N. E.
Published: February 2007

Fatigue tests have been carried out on sheet specimens, 10 in. wide by about 0·1 in. thick, containing a small central slit, and measurements made as the test proceeded of the lengths of fatigue cracks initiated by the slit. Seven common engineering materials were tested at various tensile mean and alternating stresses. Similar tests have been reported previously (Frost and Dugdale (1)† and Frost (2)) in which the tensile mean stresses were relatively low; in the present paper the effect of higher mean stresses on the rate of crack growth was investigated. It was concluded that, for values of mean stresses greater than 2 ton/in2, the rate of growth could be represented by:

where l is the crack length, σalt the nominal semi-range of alternating stress, σmean the nominal tensile mean stress and σmean ≥ σalt (i.e. stress cycle wholly tensile), N the number of cycles, and P and Q are material constants.

For mild steel and copper the rate of crack growth was independent of tensile mean stress,
General Analysis of Two-Degree-of-Freedom Instability in Machine Tools
Authors: Gurney J. P.
Published: February 2007

This paper utilizes the concept of receptances to investigate the stability of machine tools under orthogonal cutting conditions when regeneration does not take place, i.e. on the first pass, or when there is no overlapping of successive cuts. A criterion of stability is derived involving the receptances of the machine for displacements between the tool and the workpiece. The stability criterion is not derived in terms of a lumped parameter model with a limited number of modes, so that the stability of any machine can be realistically analysed.

The effect of changes in the direction of the cutting force on the stability of a horizontal milling machine is theoretically examined. Mohr's circle for receptance, analogous to Mohr's circle for stress, is introduced and used to apply the stability criterion to cases in which the normal to the cut surface changes in direction.
Coupled Periodic Motion in free Undamped Non-Linear Two-Degree-of-Freedom Systems
Authors: Henry R. F.
Published: February 2007

This paper deals with free periodic motions occurring in non-linear systems with equations of motion of the form

The existence of two types of periodic motion is established and amplitude-frequency relations are derived. An account is given of experimental tests carried out on an analogue computer. The results obtained are applicable to non-linear vibration-isolating suspensions, non-linear vibration absorbers and the non-linear vibration of imperfect bodies of revolution.
Principles of Gas-Lubricated Shaft Seals
Authors: Whitley S. , Williams L. G.
Published: February 2007

Four types of gas-lubricated seals for rotating shafts are described, each based on a corresponding type of gas bearing. These seals are the hydrodynamic disc seal (based on the spiral-groove thrust plate), the hydrostatic disc seal (based on a hydrostatic full-face thrust plate), the hydrodynamic sleeve seal (based on a hydrodynamic full journal bearing), and the hydrostatic sleeve seal (based on a hydrostatic journal bearing).

Each seal consists of two parts, a gas-bearing region and a gland region. The gas-bearing region must provide a gas film of the correct thickness between the seal surface, and this film must be sufficiently stiff to prevent excessive vibration. The gland region, which is the seal proper, must restrict the flow of gas into and out of the sealed system to a minimum acceptable standard. The theory of the gas-bearing region of the seals is based on standard gas-bearing principles and these have been summarized into a form suitable for seal application. The theory of the gland region is that of gas flow between parallel surfaces and this is described only in the viscous flow regime.

To clarify the principles of the seals, examples are given of the design of each type of seal for use on a 2-in. diameter shaft operating at 9000 rev/min with zero pressure in the sealed system.
Note on a Torsional Failure Caused by Gear Inaccuracy
Authors: Bishop R. E. D.
Published: February 2007

Some details are recorded of the failure of a turbine-driven compressor set as a result of torsional excitation due to gearing error. While serious vibrations of this sort are apparently rare, the type of system and conditions under which the failure occurred are not.
Velocity Profile Measurements on Non-Newtonian Fluids Flowing in Pipes using a Miniature Propeller Velocity Indicator
Authors: Billington E. W. , Jones J. T. , Wyllie D.
Published: February 2007

The use of a miniature propeller as a velocity indicator is described together with the calibration of the instrument over a wide range of flow velocity and viscosity. A suggested interpretation is given of the dependence of the angular velocity of the propeller on the velocity of flow.

An example is given of the use of this instrument to obtain the velocity profile of a natural ‘wax-containing’ oil, which exhibits thixotropic behaviour, and which is flowing through a wide-diameter pipe.
Numerical Analysis of the Axi-Symmetric Bending of a Toroidal Shell
Authors: Payne D. J.
Published: February 2007

Finite difference approximations are used to analyse a symmetrically loaded toroidal shell. It is shown that the equations derived by E. Reissner in terms of Hϕ r0 (the product of the radial force per unit circumference normal to the axis of revolution and the radius measured normal to the axis) and V (rotation of the meridional tangent) avoid the difficulties which occur, owing to a singularity at the pole circle of a toroidal shell, when Meissner's equations in terms of U = Qϕ r2 (the product of the lateral shear force per unit circumference and the second principal radius of curvature) and V are used (Fig. 1). A numerical example is solved with both forms of the equations. The values obtained for Hϕ, Qϕ and V differ by less than 1 per cent near the edge of the shell but in the region of the pole circle there is no correlation between the two sets of results. Comparison with Turner's analytic solution shows that the values and positions of the maxima and minima differ by up to 6 per cent and 5° respectively.
Effects of Variations in the Screw Thread Coefficient of Friction on the Clamping Force of Bolted Connections
Authors: Lambert T. H.
Published: February 2007

When load is applied to a bolted connection in the direction of the bolt axes, the residual clamping force on the joint is dependent upon the pretension of the bolt. Where bending action is also present, the fluctuating stress in the bolts may also be dependent upon the pretension. In most cases where an accurate pretension is required, the bolts are tightened by means of a torque spanner, and the pretension is then dependent upon the coefficient of friction between the screw threads of the nut and bolt. The effect of normally distributed variations in the coefficient of friction on the pretension is considered.
Discontinuity Stresses in Spherical Pressure Vessels with Cylindrical Supports
Authors: Fessler H. , Penny R. K. , Wright D. A.
Published: February 2007

The frozen stress photoelastic technique was used to determine the inner—and outer—meridional, and hoop, stresses in 13 models. Most models were subjected to internal pressure, but gravity effects were also studied. The extreme values of all discontinuity stresses are presented.

The theoretical stress distributions in two models were calculated and compared with the experimental values. Fair agreement was found.
Analysis of Centrifugal Stresses in Turbine Wheels
Authors: Haigh R. E. , Murdoch M. L.
Published: February 2007

A method of determining the stress distribution in rotating axially symmetrical systems is presented. The analysis is based on the three-dimensional equilibrium equations and is applicable to turbine wheels of appreciable thickness for which the thin disc (plane-stress) theory gives only approximate results. A convergent numerical solution using two stress functions has been obtained on a digital computer by ‘relaxing’ two governing equations.
Experiments on a Supersonic Parallel Diffuser
Authors: Martin B. W. , Baker P. J.
Published: February 2007

This paper reports the results of experimental work on a two-dimensional model of a supersonic parallel diffuser of the type used to achieve some recompression of a high-temperature jet, though in the present tests a relatively low temperature was employed. Visual observations were made of the flow patterns developed in the diffuser, together with corresponding measurements of static pressure distributions and local heat transfer rates, for a range of initial total pressures. The effect of varying the area of the diffuser cross-section, for the same upstream generating nozzle, has also been studied. The static pressure recovery across the diffuser is found to reach a maximum at the transition from a normal shock to a multiple oblique shock system of diffusion. Following a peak value near the diffuser entry, the heat transfer, which generally follows the static pressure distribution, fluctuates about relatively low values in the region of the shock patterns, but rises steadily when the flow becomes subsonic in the downstream section of the duct.
Some Experiments on the Balancing of Small Flexible Rotors: Part I—Theory
Authors: Parkinson A. G. , Jackson K. L. , Bishop R. E. D.
Published: February 2007

A theoretical balancing technique was proposed by Bishop and Gladwell (1)§ and an experimental investigation of its usefulness is reported. Experiments conducted on the laboratory scale were believed necessary before full-scale tests on large industrial rotors (such as alternator rotors) could be properly justified. The thin shafts which were used clearly showed the importance of initial bend (as opposed to mass unbalance) as a source of forced vibration. This required some additions to the original theory, and they are the subject of Part I of this paper. Part II | contains an account of the actual experiments and of the test apparatus. It is concluded that the theory is fully borne out on the laboratory scale and that comparable tests on large rotors would be justified.
Natural Frequencies of Uniform and Non-Uniform Rectangular Cantilever Plates
Authors: Plunkett Robert
Published: February 2007

Various methods of calculating the natural frequencies of flat rectangular cantilever plates are discussed, and it is shown both analytically and experimentally that relatively simple expressions based on technical beam theory give good results even for high order modes. Experimental results indicate that the mode shapes of plates of non-uniform thickness have modes so complex that a great many terms should be used in any vibration analysis, whether finite difference or Rayleigh-Ritz.
Analogue Computer Solutions of the Heat Conduction Equation
Authors: Freed N. H. , Rallis C. J.
Published: February 2007

Exact solution of many heat conduction problems in engineering is frequently tedious and seldom warranted. Many analogue methods have in consequence been developed.

For steady-state problems the conducting sheet and electrolytic tank types appear to be the most convenient in use.

The solution of non-steady-state problems is generally best achieved through indirect analogy methods, whereby the partial differential equations characterizing the phenomenon are replaced by an approximating set of finite difference equations. Various networks for achieving this are reviewed and compared from the standpoint of economy, convenience and accuracy.
Interstage Regeneration in the Gas Turbine Cycle
Authors: Weir C. D.
Published: February 2007

A discussion of the thermodynamics of interstage regeneration in the elastic fluid cycle is presented for the case of one regenerator. Results are derived for both pumped and cascaded regeneration in real (irreversible) cycles with pressure drops. It is shown that in each case an optimum extraction mass ratio and an optimum extraction temperature exist, the latter depending on the pressure ratio.

The calculation of some examples indicates that interstage regeneration is unlikely to prove financially attractive except possibly in the case of cascaded regeneration over a limited range of pressure ratios.
Deformation of Uniformly Loaded Beams Obeying Complex Creep Laws
Authors: Anderson R. G. , Gardner L. R. T. , Hodgkins W. R.
Published: February 2007

The deformations of uniformly loaded, simply supported beams are derived for a simple creep law of the type

where is the secondary creep rate, ρ is the applied stress and n is the creep index. The solution is extended to include a yielding behaviour such that ρ ≥ Y where Y is a yield stress. The deformations are found to be relatively insensitive to the value of n so long as the strain rate is known at a ‘representative stress’ in the beam and the representative stress is less than about 95 per cent of the yield stress. The concept of representative stress is used to estimate useful upper and lower bounds for the deformations of a simply supported beam composed of a material with a complex creep law in which the stress index n is continually increasing with increasing stress.

Similar results for cantilevers and clamped beams suggest that the representative stress concept is useful for the solution of many problems involving deformations under complex creep laws or for problems in which a minimum of creep information can be obtained.
Analysis of Turbulent Bearing Films
Authors: Reynolds A. J.
Published: February 2007

In studying the performance of laminar bearing films one need give little attention to the details of the internal flow. The velocity distribution is so simply related to the pressure gradient that one is able almost immediately to concentrate on the pressure distribution. But for a turbulent film the situation is quite different. No simple laws are known relating the volume flow through the film to the pressure gradient and relative velocity. A thorough study of the motion within turbulent films must be made before their characteristics as bearing films can be assessed.

Thus this work falls into two parts. In Part I the basic analysis of two-dimensional turbulent channel flows is given. The application of its results to bearing analysis is treated in Part II.
Forced Undamped Non-Linear Vibrations of Imperfect Circular Discs
Authors: Williams C. J. H. , Tobias S. A.
Published: February 2007

The forced vibrations of modes consisting of at least one nodal diameter and an arbitrary number of nodal circles are investigated. The case when the position of the exciting force coincides with a node of one of the preferential configurations is examined. It is shown that a stationary harmonic force may excite a stationary vibration with a fixed nodal pattern, or a ‘beating’ travelling wave, depending on the conditions of excitation. The stability of vibration of modes consisting of fixed nodal patterns is investigated.
Extraction of Data for a Sub-System from Resonance Test Results
Authors: Pendered J. W. , Bishop R. E. D.
Published: February 2007

A technique is explained and illustrated whereby the response of one sub-system of a compound system may be extracted from the measured response of the whole. The system examined consists of two sub-systems, a beam and a concentrated mass, linked by a common co-ordinate at the point of excitation. The results obtained from this composite system are then analysed and the data that are required from a resonance test on the beam alone are extracted.
Transient Response of an Hydraulic Servomechanism Flexibly Connected to An Inertial Load
Authors: Davies R. M. , Lambert T. H.
Published: February 2007

The transient response of a powerful hydraulic servomechanism, flexibly connected to an inertial load is investigated theoretically and experimentally. The results indicate that a linearized fifth-order transfer function, taking into account inertial load, compressibility, leakage, and structural flexibility and damping, gives a reliable indication of the main characteristics of behaviour of this type of control in such a realistic environment. Extension of the theory to include the effects of the principal non-linearity, Coulomb friction, by simulation on an analogue computer increases the viability of the analysis.

It is found that the response is of an oscillatory, biharmonic character; the low-frequency component of which is attributable mainly to effects external to the jack and the high-frequency component to internal effects. Consistently, it is found that the subsidence ratio of the former is sensitive to structural damping and of the latter to Coulomb friction and leakage.
Tool Forces and Tool-Chip Friction in Orthogonal Machining
Authors: Wallace P. W. , Boothroyd G.
Published: February 2007

An examination of previous work on metal cutting reveals that the normal characteristics of sliding friction do not hold for the friction between chip and tool. Several explanations for the variation in coefficient of friction have been proposed; however, none is entirely-consistent with experimental evidence. In the present work an analysis of the physical variables in metal cutting is presented. This allows the force acting on the tool rake face to be separated from the force acting in the region of the tool nose. Experimental results obtained when cutting an aluminium alloy are presented; in obtaining these, the tool forces were measured with a strain-gauge type dynamometer. The results show that two mechanisms of friction exist on the chip-tool interface: (1) Over part of the contact area between chip and tool ‘sliding’ friction occurs in which the coefficient of friction is constant; (2) Over the remainder of contact, ‘sticking’ friction occurs in which the frictional stress remains constant and independent of normal pressure. This model of combined sticking and sliding friction is verified by examination of the contact conditions at the chip-tool interface after the cutting action has been abruptly stopped; a theoretical analysis based on this model shows good agreement with the experimental results.
The Design of Rotors to Have the Minimum Weight Consistent with a Required First Critical Speed
Authors: French M. J.
Published: February 2007

A section is being set aside in the Journal of Mechanical Engineering Science for the publication of Research Notes and contributions are invited for inclusion in future issues. These should not exceed 1000 words in length and should be accompanied by not more than two illustrations. They need not necessarily be related specifically to any previously published paper in the Journal, as contributions on these lines will continue as before to be published as Communications. The first two such Notes are published below.
Vibrations of Pre-Twisted Cantilever Blading Allowing for Rotary Inertia and Shear Deflection
Authors: Carnegie William
Published: February 2007

The general equations of motion of a pre-twisted cantilever blade, mounted encastré at the root, are derived in a previous paper (1) by the author. Secondary effects are not dealt with although there are three such effects to be considered. The effect of torsion bending is the subject of a subsequent report (2). The present paper derives the general equations of motion of a pre-twisted cantilever blade allowing for torsion bending, rotary inertia and deflections due to shear. The potential and kinetic energy relationships are given and by use of the standard variational approach the equations of motion and corresponding boundary conditions are deduced.
Analysis of the Cup-Drawing Process
Authors: Woo D. M.
Published: February 2007

An analysis has been developed for the study of the cup-drawing process which includes radial drawing over a die and stretch-forming over a punch. Theoretical results were obtained on a Pegasus computer.

The analysis for radial drawing has been limited in this investigation to the case of drawing with a pressure blank-holder although similar analysis can also be made for the case of drawing with a clearance blank-holder. For the brass and mild steel used, the agreement between the theoretical and experimental results is generally satisfactory.

In the analysis of stretch-forming over a punch head, two cases were considered: one for a 4-in diameter flat-headed punch with 1-in profile radius and the other for a 2-in diameter spherical-headed punch. The material used was brass. Theoretical strains based on simplified conditions in stretch-forming were obtained and compared with the experimental results. Agreement is good between the theoretical and experimental circumferential strains but the correlation between the thickness strains is unsatisfactory. For possible improvement in the theoretical results, a more exact analysis has been suggested.
Quasi-Theoretical Method for Calculating the Rigidity of Multi-Pass Tube Plates
Authors: Duncan J. P.
Published: February 2007

Tube plates of heat exchangers often consist of circular elastic plates into which tubes are secured by welding or swaging. The holes in the plate into which the tubes are fixed are arranged in zones within the outer boundary of the plate to suit the nesting of the tubes.

Such tube plates are flexed principally by a hydrostatic pressure differential. In this action they function as many-times multiple-connected elastic plates and exact analysis is greatly complicated by the many internal boundaries.

Since such boundaries are normally grouped in the form of zones of regularly arrayed, identical and uniformly pitched holes, the notion of ‘equivalent elastic constants’ as discussed in a related paper, reference (6), can be used to describe the average behaviour of such drilled zones. The number of significant internal boundaries can thus be reduced to the number of zones corresponding with the number of nests of tubes, usually two or four.

The boundaries of the nests usually possess symmetries about the diameters of the plate. Using this fact together with the notion of equivalent elastic constants a method is developed in both detailed and simplified form for predicting theoretically, through an integral equation, the flexural behaviour of characteristic types of tube plate with encastré and simply supported boundaries.

These theoretical methods were tested experimentally on several models whose behaviour was recorded by means of interferometry. Agreement between theory and experiment was established within acceptable limits.