Journal of Mechanical Engineering Science

The partial differential equations of motion are obtained for a helical spring subject to a static axial force, the typical element of the spring having six degrees of freedom. The wire cross-section can be any doubly symmetrical shape. The overall transfer matrix is calculated and its application is discussed for obtaining the response to forced sinusoidal vibration. Natural frequencies are found from the transfer matrix by iteration. Comparisons are made with published experiments on the natural frequencies of helical springs, made from round wire, with and without a static axial force. Comparison is also made with published theory for the static buckling of helical springs. Information is given on the effect on the natural frequencies of the static axial force, helix angle, number of active turns, ratio of helix to wire diameter, Poisson's ratio, shear coefficient, and the end conditions. The calculation of the normal modes is discussed.

In this paper, a general numerical solution to the elastohydrodynamic point contact problem is presented for moderate loads and material parameters. Isobars, contours and regression formulae describe how pressure and oil film thickness vary with geometry, material properties, load, and squeeze velocity, when the rolling velocity vector is at various angles to the static contact ellipse long axis. In addition, the EHL behaviour under spin is examined. The theoretical predictions of film thickness compare favourably with other numerical solutions to the point contact problem, as well as with experimental results which use the optical interferometry method to find film thickness and

A procedure is described for predicting the recommended insert thickness which will result in minimizing the thermal resistance of a pressed contact between fiat, non-wavy, surfaces. The analysis is based upon the assumption of ideal plastic asperity deformations occurring at the interfaces formed between randomly high rough surfaces and the insert material. Experimental measurements of the thermal resistances for aluminium-tin-aluminium and stainless steel-tin-stainless steel, mechanically loaded assemblies corroborate within experimental error the predictions from the theory, and hence validate the analysis.

Vortex diodes handling liquids are subject to the effects both of cavitation and Reynolds number. The apparent complexity of their characteristics makes design and simulation difficult. To some extent, however, this complexity is artificial and can be reduced.

The effect of cavitation is most severe in the forward state. The usual characterization in terms of Thoma's cavitation number (based on pressure drop and downstream pressure) obscures a much simpler relationship using the upstream pressure explicitly. This yields simple equations which cover the cavitating regime. The non-cavitating characteristics are shown to be well predicted by established data on the operation of diffusers. Experimental data vindicating this is taken from Zobel, Syred et al, and our own experiments.

Cavitation in the reverse state is not simplified but it is much less important for the diodes quoted. The practical implications of these results in diode pump applications are examined and quantified.

This investigation is devoted to studying the thermal and hydrodynamic stability of the conduction regime of natural convection of a fluid with a nonlinear density temperature relationship in a slender slot with different, but constant, temperature walls. Linear perturbation techniques are applied for the transverse two dimensional disturbances to derive a set of two coupled twelfth order partial differential equations; the Galerkin method was used to solve the eigenvalue problem. The results of this analysis indicate that this flow is much more susceptable to thermal stability than to hydrodynamic stability for Prandtl number, Pr > 3·2. On the other hand for Pr < 3·2 the reverse is true.

Furthermore, both shear and bouyant mode characteristics are determined for a wide range of Pr.

The dynamic stability behaviour of a tapered beam has been studied using a finite element analysis. The instability zones of the parametric stability diagram have been discussed for the entire ranges of static and dynamic load factors. It has been observed that at high values of static load and beyond a particular value of the dynamic load factor, the periodic solution of the Mathieu equation does not exist in the principal region. This leads to unstable behaviour due to large displacement of the beam due to increasing values of static and dynamic load factors.

It is shown that the average Reynolds equation for rough surfaces using an incompressible lubricant derived by Patir and Cheng (1)§ can be used for a compressible lubricant if the surface structures of both surfaces are the same. The average Reynolds equation is applied to an infinitely long gas journal bearing to find the hydrodynamic load capacity. The effect of the roughness parameter and the surface pattern parameter on the hydrodynamic load is also investigated.

Van de Vegte (1)‡ discusses the balancing of a flexible multi-disc rotor supported in two bearings, using two motorized balancing heads. The underlying idea of the motorized balancing head is used in the present paper, but with a completely different line of theoretical reasoning. Modal analysis suggests that, provided certain requirements as to the nature of the bearings are met, the approach described by van de Vegte may be unnecessarily complicated, in that only one motorized balancing head need be used, while neither the reference to ‘discs’ nor the restriction to two bearings may be needed.

Multidimensional computational analysis of fluid flow is usually done by segmented iterative methods, as the equations sets generated are too large to permit simultaneous solution. Frequently the need arises to compute values for variables which must remain bounded for physical reasons. In two-phase computation, for example, the volume fraction is restricted to values between 0 and 1, but iterative procedures often return intermediate values which violate these bounds. It is fairly straightforward to prevent negative values, however no satisfactory method of imposing the upper limit has been published. A method of smoothly applying the limit in reversible fashion is outlined in this note.

A flexible inextensible horizontal belt is assumed to be formed, by closely spaced vertical push rods, into a traveling sine wave. A spherical object resting at the bottom of a trough will tend to be convected with the trough as the wave travels. The dynamic stability of such wave-convection transport is considered. Assuming the wave to be shallow, the governing nonlinear equations are expanded (through second order) in the ‘shallowness parameter’, and thus reduced to a single equation, essentially of forced Duffing type, which is integrated numerically, over the parameter space of practical interest, to yield a stability criterion.