bluuebunny/crossref_metadata_2025_split 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.
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.
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.
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.
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.
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.
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.
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.
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.