Journal of Mechanical Engineering Science

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.

In an earlier paper (1)†, the author discussed the nature of pressure pulsations in suction systems of free-piston gas generators, and in particular various forms of pulsation damping devices.

A theoretical approach was based on a simple linear treatment of the system, i.e. (1) regarding all pressure pulsations as small in relation to the mean pressure on which they are superimposed, (2) treating dissipative elements (pipe friction or concentrated restrictions) as having linear pressure drop-velocity relationships about the mean flow condition, and (3) treating all distributed elements as having wave motion in accordance with small wave (2) or acoustic theory (rather than the non-linear finite wave theory (3) (4)).

Although the physical conditions in compressor delivery systems are very different from those in gas generator suction systems, a similar theoretical approach, verified by acoustic model tests, has been found both to provide a good insight into the problem, and to give an acceptably accurate quantitative indication of pressure pulsation amplitudes.

For this purpose systems have been divided into: (1) lumped impedance systems, (2) distributed impedance systems.

Master and slave systems utilize two types of hydrostatic bearing in order to provide high load capacity in conjunction with non-redundant location by rigid-film hydrostatic bearings. Master bearings are controlled both by applied thrust and by their clearance, and they also control the thrust in the slave bearings which act independently of their own clearances. A journal bearing is used to illustrate analysis of bearing systems, redundant locations, and master and slave systems. A general analysis of master and slave systems is given and a design procedure, advantages, fields of application, and design calculations for individual bearings are outlined in the text and appendixes.

The paper deals with a study of the development of anisotropy and the Bauschinger effect in cold rolled aluminium. In the first instance, the development of a yield criterion considering both of these phenomena is discussed. By following a recent development by Yoshimura, a criterion involving only two parameters, one for anisotropy and the other for the Bauschinger effect, is developed. Considering the simple homogeneous rolling deformation model of Orowan, the yield criterion is applied to the case where cold rolled metal is subsequently tested in tension and compression at various orientations.

Experimental procedures are described and the method of correlating the experimental results with the yield criterion is discussed. As a result of the analysis of the experimental results, it may be concluded that the yield criterion provides satisfactory correlation with experiment. The anisotropy parameter and a Bauschinger modulus are then specified in terms of rolling strain and the order of their magnitude considered.

The last part of the paper is concerned with a discussion of additional factors which have a bearing on the results obtained. In the first place, the question of inhomogeneous deformation is considered. One of the consequences, the development of residual stresses, is shown to have little effect. However, additional evidence shows that the mode of deformation exerts a considerable influence on the Bauschinger modulus. It is concluded that anisotropy is probably not greatly influenced by the details of deformation, but the manifestation of the Bauschinger effect certainly is.

Flow parameters are presented for journal and circular pad hydrostatic bearings supplied with oil through a central port shaped as a regular polygon with rounded corners. Load parameters are evaluated for the circular pad bearing. The analysis, by the method of conformal mapping, is extended to the rectangular port and also yields solutions for narrow oilways radiating from a central point in the bearing.

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.

Previous investigations of the flow of gases through sudden area changes in pipes are briefly reviewed, both unsteady and steady flow conditions being considered.

The present paper concerns the effects of such area changes on single pressure waves of finite amplitude, and covers incident wave amplitudes greatly in excess of those previously investigated.

Theoretically, the flow at the area change is assumed to be quasi-steady and one-dimensional, and two alternative treatments are presented. These are based respectively on reversible adiabatic (isentropic) and, more accurately, irreversible adiabatic conditions.

Experiments using a simple shock tube confirm the validity of the more accurate theoretical treatment over the range of area and incident pressure ratios considered, namely, 8.1 and 2.4 respectively. The theoretical treatment based on the assumption of isentropic flow at the section change, however, is inadequate in some respects. Discrepancies between theory and experiment are observed when considering, firstly, the reflected wave at an enlargement and, secondly, the transmitted wave at a contraction.

Steady flow experiments in which the discharge coefficient for flow through a sudden contraction is measured are also described, this coefficient being required in the theoretical analysis.

Some recent work on fretting fatigue in lap joints has shown that certain treatments of the joint contact surfaces greatly improve the fatigue life of the joint, and suggests that maximum benefit may be obtained by arranging for force transference within the joint to take place only by frictional resistance.

A simple theoretical analysis of a simple lap joint is here presented which estimates the frictional energy dissipation, and concludes that, for any pressure distribution imposed along the joint faces by the rivet clamping force, the damping capacity of the joint is a maximum when force transference is only by friction throughout the joint.

A method is presented for the solution of boundary value problems in the secondary creep of circular cylindrical thin shells subject to axisymmetric loading. Approximate stress resultant-middle surface deformation relations based on an n-power creep law are used. Solutions are given for deformation rates and stress resultants in a long cylinder with fixed ends under uniform radial loading and uniform internal pressure. Quantities important for design purposes are found to be reasonably well predicted from the linear elastic solution for a useful range of n values.

The well-known logarithmic friction factor diagram for laminar pipe flow can be extended in the following two respects:

For application to non-Newtonian fluids, by incorporating in the plot a modified form of the consistency curve for a given material. Methods are discussed of obtaining these curves, and of transforming them into the required shape.

A shaft-rotor system which has a symmetrical nonlinear restoring force exerted on the rotor when it is radially displaced is analysed. Solutions which predict harmonic whirl are obtained and their stability is investigated. The effect of viscous friction in the rotating members is considered and, as a result of the nonlinearity, a whirl is shown to occur at frequencies which correspond to the free undamped vibrations of the system rather than at the synchronous speed.