Parametric Instability of Tapered Beams by Finite Element Method

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.

On the Possibility of Balancing Rotating Flexible Shafts

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.

Oil Film Thickness and Pressure Distribution in Elastohydrodynamic Point Contacts

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 Method of Limiting Intermediate Values of Volume Fraction in Iterative Two-Fluid Computations

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.

Minimizing the Thermal Resistance of Pressed Contacts

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.

Dynamic Stability of Wave-Convection Transport

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.