Local Elastic Deformation Research Articles

An Inverse Solution to the Point Contact EHL Problem Under Heavy Loads

A set of computational results of the point contact EHL problem under heavily loaded condition is presented in this paper, and the numerical scheme for the inverse solution of the Reynolds Equation is developed. By using a deformation matrix to calculate the local elastic deformation and its inverse matrix to modify the pressure distribution, both the convergence and the stability of the numerical method are satisfactory. The examples of calculation adopted have been extended from Hamrock and Dowson’s cases into the operating region of heavy load. The results obtained have shown the effects of speed, load, and choice of materials on the film thickness, and have proved Hamrock and Dowson’s formulae for estimating film thicknesses to be accurate under heavily loaded condition.

Effect of local elastic wall deformations on the interaction between floor slabs and flanged shear walls

A finite-element analysis is made of the interaction between laterally loaded flanged shear walls and floor slabs in cross-wall structures. Particular attention is paid to the influence of local elastic wall deformations on the effective width and coupling stiffness of the slab, and on the critical bending moments in the slab. Design curves are presented to allow a rapid assessment to be made of these quantities for preliminary design purposes. The work is an extension of an earlier study of coupled plane walls.

Influence of Door Openings on Effective Slab Width

A finite element analysis is made of the interaction between floor slabs and laterally loaded shear walls that include a doorway opening for internal circulation within apartments. Particular attention is paid to the influence of local elastic wall deformation on the effective width and coupling stiffness of the slab. The influence of the size and position of the doorway opening is examined for a typical wall-slab configuration. It is concluded that the presence of a doorway opening does not significantly affect the effective slab stiffness.

Variable Degree-of-Freedom Component Mode Analysis of Inertia Variant Flexible Mechanical Systems

A method is presented for transient dynamic analysis of mechanical systems composed of interconnected rigid and flexible bodies that undergo large angular displacements. Gross displacement of elastic bodies is represented by superposition of local linear elastic deformation on nonlinear displacement of body reference coordinate systems. Flexible bodies are thus represented by combined sets of reference and local elastic generalized coordinates. Modal analysis and sub-structuring of the local elastic system identifies all modes and allows for elimination of insignificant modes. Equations of motion and constraints are formulated in terms of minimum mixed sets of modal and reference generalized coordinates, and dynamically adjusted to a time and interia-variant eigenspectrum. A flexible mechanical linkage and a tracked vehicle with a flexible gun tube are simulated to illustrate the method.

The elastohydrodynamic lubrication of piston rings

The piston seal that separates the hostile environment of the combustion chamber from the crankcase that contains the lubricant is an essential machine element in reciprocating engines. The sealing force pressing the piston rings against the cylinder liner varies with the combustion chamber pressure to form an effective self-adjusting mechanism. The conjunctions between piston rings and cylinder liners are thus subjected to cyclic variations of load, entraining velocity and effective lubricant temperature as the piston reciprocates within the cylinder. Recent theoretical and experimental studies have confirmed that piston rings enjoy hydrodynamic lubrication throughout most of the engine cycle, but that a transition to mixed or boundary lubrication can be expected near top dead centre. The purpose of the present paper is to examine the suggestion that elastohydrodynamic lubrication might contribute to the tribological performance of the piston seal, particularly near top dead centre. The mode of lubrication in eight four-stroke and six two-stroke diesel engines is assessed in terms of the dimensionless viscosity and elasticity parameters proposed by Johnson (1970), and the associated map of lubrication régimes. The survey indicates unequivocally that elastohydrodynamic action can be expected during part of the stroke in all the engines considered. In the second part of the paper a detailed examination of the influence of elastohydrodynamic action in one particular engine is presented to confirm the general findings recorded in the study of lubrication régimes. Current analysis of the lubrication of rigid piston rings already takes account of the variation of surface temperature along the cylinder liner and its influence upon lubricant viscosity. It is shown that, when the enhancing influence of pressure upon viscosity is added to the analysis of rigid piston rings, the predicted cyclic minimum film thickness is more than doubled. Full elastohydrodynamic action, involving both local distortion of the elastic solids and the influence of pressure upon viscosity, results in a fourfold increase in film thickness. It is further shown that it is necessary to take account of the variation of squeeze-film velocity throughout the lubricated conjunction at each crank angle if reliable predictions of film shape and thickness are to be achieved. It is thus concluded that the wave of elastic deformation, which ripples up and down the cylinder liners many times each second in diesel engines, together with the associated local elastic deformations on the piston rings themselves, combine with the influence of pressure upon lubricant viscosity to enhance the minimum oil film thickness in the piston seal by elastohydrodynamic action.

A Coordinate Reduction Technique for Dynamic Analysis of Spatial Substructures with Large Angular Rotations∗

ABSTRACT A substructuring technique is presented for transient dynamic analysis of systems composed of interconnected rigid and elastic bodies that undergo large angular displacements. Displacement of elastic bodies is represented by superposition of local linear elastic deformation on large displacement of body reference coordinate systems. Elastic bodies are thus represented by combined sets of reference and local elastic generalized coordinates. Modal analysis and substructuring of individual elastic components allow for elimination of insignificant modes. Equations of motion and constraint are formulated in terms of mixed sets of modal and reference generalized coordinates. Planar and spatial linkages with flexible elements are presented to illustrate use of the method developed.

On the development of fluid trapping beneath deformable fluid-cell membranes

A quantitative theoretical model is developed to describe the time-dependent draining of an initially uniform-thickness fluid squeeze film between an infinitely flexible membrane-bound fluid cell and a planar rigid surface or between two symmetrically loaded cells subject to impulsive loading. The solution of the coupled nonlinear membrane-fluid-film equations shows that two characteristic times and lengthscales are required to describe the membrane deformation and draining behaviour of the fluid film. The early-time behaviour is strikingly different from that predicted by elastohydrodynamic squeeze-film theory (Christensen 1962), where the local elastic deformation of the boundary is not controlled by membrane tension but is pro-portional to the local film pressure. While fluid trapping occurs in both cases, a bidirectional flow is set up during the early-time period in the membrane squeeze film owing to the establishment of an off-axis pressure maximum near the edge of the near-contact area. Fluid is driven radially inward, causing upwelling of the membrane in the central region, and driven radially outward near the edge of the contact area., causing this region to form a narrow fluid gap. After the narrow-edge region hasformed, the off-axis pressure maximum gradually disappears and is replaced by a pressure plateau in the interior and a radial outflow at all locations that is similar to the elasto-hydrodynamic squeeze film. The present problem is closely related to the fluid films studied by Hartland (1967, 1968, 1969), Jones & Wilson (1978) and others when a, small spherical particle or fluid droplet rises or settles under gravity towards a uniform-tension fluid-fluid interface. These studies have theoretically and experimentally examined the long-time drainage of the film after the narrow edge region has formed and the fluid-trapping phenomenon is established. The solutions to the initial-value problem described herein show how this asymptotic quasi-steady drainage state is reached.A simple experiment has been constructed to confirm qualitatively the theoretically predicted short-time behaviour. Experimental photographs graphically illustrate the gradual thickening of the lubricating layer near the origin and the formation and draining of the edge region as predicted by the membrane squeeze-film theory.

Analysis of deformation and contraction in cylindrical crystals due to dispirations or dislocations

Cylindrical crystal structures are common in biology. The shape changes and movements of cylindrical crystals are basic to the understanding of the contractile mechanisms in biological systems such as tobacco mosaic viruses and the tail sheath of T-even bacteriophages. It has been suggested that the concept of defects in crystal physics can be applied to study these contractile mechanisms. The defect believed to be responsible for the shape changes of cylindrical crystals is known as a dispiration. Dispirations are characterized by the shear displacement on the slip plane through a screw symmetry operation. The elastic field of a dispiration can be decomposed into its translational (dislocation) and rotational (disclination) components. The magnitude of the translational and rotational displacements in a cylindrical crystal has been related to the crystal structural parameters. The passage of a dispiration along a helical plane in a cylindrical crystal can induce one of two types of shape changes. In one type, only the disclination component of the dispiration contributes to contraction, whereas in the other type, both the disclination and dislocation components are responsible for the shape change. Estimates of the magnitude of contraction are made in terms of the dimensional and structural parameters of the cylindrical crystal. The reversal of the direction of helical slip results in extension instead of contraction of the cylindrical crystal. The local elastic deformation of a dispiration dipole situated on the helical plane of a cylindrical crystal is examined. It has been shown that, for the first type of deformation mentioned above, closed form solutions of the stress field can be obtained by superposing the stress fields of two dispiration dipoles with slip planes parallel and normal to the cylinder axis, respectively. The approximations of shallow shell theory are adopted in the analysis. Future problems of biological interests are identified.

Non-linear mechanical response of various metals. III. Swift effect considered in relation to the stress-strain behaviour in simple compression, tension and torsion

For pt.II see ibid., vol.10, no.4, p.533 (1977). The correlation of the stress-strain behaviour in simple compression, tension and torsion is considered for various metals in relation to the Swift (1947) effect, here observed as the permanent lengthening of a tubular specimen along the principal axis about which it is being twisted. The proposed correlation is based on an incremental-type constitutive equation for an isotropic incompressible strain-hardening elastic-plastic solid with large deformation. Formulation of the proposed constitutive equation involves a modified Mises yield condition and the assumption that the total deformation gradient can be decomposed into a matrix product of the local elastic and plastic deformation tensors. Since the Swift effect appears to be absent at high strain rates, the metals of present interest should appear stronger at high strain rates, a conclusion in accord with the observation that the dynamic yield stress is frequently observed to be higher than the static yield stress in all three simple modes of deformation.

Contact vibrations of a wheel on a rail

When a wheel rolls on a rail with a randomly wavy surface, the random waviness gives rise to a displacement input to the wheel and rail with a significant high-frequency (f>100 Hz) spectral content. This displacement input excites the contact resonance of the system, wherein the mass of the wheel and an “equivalent mass” of the rail vibrate on the nonlinear contact spring. The purpose of this paper is to develop an analytical model for these high-frequency contact vibrations. The wheel is assumed to undergo only rigid-body motions, apart from the localized elastic deformation near the contact region. The rail is modeled as an infinite beam on a continuous, point-reacting foundation. With the rail roughness being assumed to be a locally stationary, Gaussian random process, a complete solution is presented to the linearized problem. Three phenomena of interest are investigated in detail: plastic deformations, loss of contact, and the formation of corrugations on the rail. The effects of various wheel and rail parameters on these phenomena are explored.

Further Studies on the Local Elastic Deformations of Honeycomb Faceplate Subjected to Uniaxial Compression

Further Studies on the Local Elastic Deformations of Honeycomb Faceplate Subjected to Uniaxial Compression

The Distribution of Contact Pressures in the Rolling of Metals

A comparison is made between the experimentally determined contact pressure distributions obtained on square bars and flat strips. The former showed double peaks in the pressure, one near entry and the other near the roll center line. A pressure peak is obtained near the center line only for strip-rolling. Two independent analyses were made. One allowed the double peak for the square bars to be predicted with fair accuracy from stress-strain data. The second, based on the local elastic deformation of the rolls, also showed the transition in pressure distributions from billet to strip-rolling.