Journal of Mechanical Engineering Science

Certain substances float on the surfaces of gaseous fluidized beds and others sink. This phenomenon has industrial applications in separation by creaming and sedimentation. To help the development of these applications the author measured the drag on metallic spheres falling through various fluidized beds of glass beads and certain granular powders. The meta***llic spheres were attached to a nylon thread which passed over a pulley system. Different balance weights were attached to the other end of the thread to produce different uniform velocities of fall. The friction of the system and the buoyancy of the immersed metallic spheres were predetermined. The drag on the sphere was then the only unknown. It was found that the drag is a function of three dimensionless groups, namely Reynolds number, Froude number and the ratio of the diameter of the metallic spheres to the mean diameter of the glass beads or powders forming the fluidized beds.

For spheres above a certain diameter deviation occurred in the measurement of the drag owing to wall effect.

The thermal stresses in axially symmetrical elastic bodies with irregular boundaries can only be obtained using finite difference techniques. Hoyle demonstrated that a solution can be computed by using the two-diagram technique but the two stress functions used have proved to be difficult to handle. These difficulties are analysed and two other stress functions are suggested which have several advantages, one of which is that these functions converge satisfactorily when completely relaxed alternately. The boundary conditions which these functions must satisfy have been rationalized and a new approach to boundaries developed which removes the worst of the difficulties formerly associated with curved boundaries.

Recent work by the authors and others on the lubrication of elastic rollers is briefly reviewed. The full effects of speed over a wide range and of lubricant compressibility are presented for the first time. Speed is shown to be the most important variable in the problem. Compressibility has little effect on the film thickness, but it may alter the pressure distribution appreciably.

A differential equation for the torsional vibration of a uniform rod of non-circular section is derived which takes into account the longitudinal stress and inertia which arise from the warping of the cross-section. The boundary conditions relevant to the problem are also obtained. Curves showing the dispersion of torsional waves in rods of rectangular section as predicted by this theory are given and a comparison is made with the results of more simple torsion theories which either neglect the longitudinal stress and inertia effects or which take account of only one or other of them. Experimental resonance tests on rods of rectangular section for various side ratios are used as a basis of comparison with the theory for relatively long wavelengths and good agreement is found.

A shear plane theory of hot rolling is proposed, based on the well-known observation of localized deformation during the rolling process.

Equations of simple form in terms of yield stress and geometric functions enable roll load and torque to be readily evaluated with or without tensions.

Comparison with the experimental results of Wallquist suggests that the theory gives a more satisfactory indication of the influence of the R/h ratio on load and torque than does the Sims analysis.

Equations are presented in four forms:

the general case with tensions;

A method is presented for predicting the flexural behaviour of circular plates supported in elastic mountings. When loaded, such plates acquire a boundary condition intermediate between a simply supported and encastré condition. If, is as often the case, a relation Mr / dw/dr= A exists between the moment exerted on the mounting by the plate, Mr, and the slope produced in the mounting, dw/dr, the plate deflects like a simply supported plate having an ‘effective Poisson's ratio’ equal to Aa/D+ρ where ρ is the natural Poisson's ratio. This has been demonstrated both theoretically and experimentally and related to the existence of points of inflection in simply supported plates.

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.

Matrix techniques for the solution of natural frequencies of a torsional system are proposed for their simplicity and easy manipulation. The tedious calculations in obtaining a dynamic matrix are alleviated by evolving a general expression for dynamic matrix for fundamental mode of a multi-degrees of freedom straight torsional system.

Further, the dynamic matrices for engine systems having four to eight cylinders with equal moments of inertia per cylinder line and equal shaft stiffnesses between the cylinder centres are deduced from a general expression. They are iterated upon five times to obtain expressions for the fundamental frequency parameter, which are further used to obtain the relative amplitudes and the frequency parameter of different engine systems. The results obtained by five times iteration are in close agreement with the exact values.

A theory for the development of the axial and peripheral velocity profiles in the early stages of an axial-flow compressor is presented. The theory assumes the existence of a stall-zone in the corner formed by the convex surface of each blade and the annulus wall. The extent along each blade of this stall-zone is assumed to be related to the theoretical annulus boundary layer thickness; equations are derived for predicting its growth through the blade roots and tips. The conditions at the blade ends are determined from the theory of a two-dimensional stalled cascade and the outlet angle variation is determined by momentum mixing. Actuator disc theory is then used to find the resulting flow. The predictions of this method are compared both with experimental results obtained from a three-stage compressor and with the predictions of secondary flow theory in which both loss and blade row entry velocity profile are taken from experiment. Somewhat better agreement between the stall-zone theory and experiment is found and to make the theory useful for designers the determination of a single parameter from experiment is indicated.

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.

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.