Contact Load Distribution Research Articles

Numerical simulation of growth pattern of a fluid-filled subsurface crack under moving hertzian loading

Cracking of a fluid-filled subsurface crack is studied by means of the distributed dislocation technique within the framework of two-dimensional linear elastic fracture mechanics. The Griffith crack was initially opened by the application of hydrostatic pressure of an incompressible fluid within the crack. A moving Hertz line contact load distribution is applied at the surface of the half-plane in the presence of friction. The stress intensity factors at the tips of the fluid-filled crack are analyzed with the restriction that due to the fluid incompressibility there is no change of the crack-opening volume. When the crack starts to propagate/kink, numerical results show that the internal fluid pressure will be relieved, and as the ratio of the branched crack length to main crack length increases, the elastic strain energy release rate decreases. The crack growth is assumed to be arrested when the energy release rate is below a certain value. Based on the energy criterion, predictions are attempted for determining the load position where the crack propagation/kink commences as well as the growth increment of the branch crack before it is arrested. A step-by-step crack path is constructed to simulate the growth pattern of the fluid-filled crack under moving Hertzian loading.

Fixturing analysis methods for calculating the contact load distribution and the valid clamping regions in machining processes

Fixturing analysis methods for calculating the contact load distribution and the valid clamping regions in machining processes

Fixturing analysis methods for calculating the contact load distribution and the valid clamping regions in machining processes

In the present work, two analysis methods for analysing fixturing systems in machining processes are presented in order to determine the most suitable clamping regions. The first involves calculating the contact load at the fixture-workpiece interface using a simple and direct mathematical tool, which simplifies the deformation minimisation problem. The second method starts from the contact load data obtained and solves several cases in which the clamping position varies. From these data, it is possible to ascertain the interpolating equations, where the load contact is defined as a function of the clamping position. Then, the border curves which limit the valid clamping regions are calculated by imposing two fixturing conditions on the interpolating equations.

Relationship between Growth of Rolling Contact Fatigue Cracks and Load Distribution

The relationship between growth of rolling contact fatigue cracks and load distribution on an inner ring of the radial rolling bearing was investigated by a new acoustic emission (AE) source location method. The histograms of cumulative AE events at possible AE source positions located in rolling contact fatigue tests were compared with the location results given by a numerical simulation. In many tests, the location histograms were not symmetric and most of the peaks in the histogram were distributed behind the actual AE source position. These corresponded to the simulation where the effective area for propagation of the fatigue crack deviated to the entrance side for the rotational direction within the loading zone. From the comparison, it became clear that the fatigue crack had a tendency to propagate in a narrow area deviating to the entrance side in the early stage of its growth and the area spread to the exit side gradually with the growth process from the initiation of the fatigue crack to an appearance of spoiling. Presented at the 55th Annual Meeting Nashville, Tennessee May 7–11, 2000

Static Rolling Bearing Models in a C.A.D. Environment for the Study of Complex Mechanisms: Part II—Complete Assembly Model

This is the second part of two companion papers, the first of which is “Static Rolling Bearing Models in a C.A.D. Environment for the Study of Complex Mechanism: Part I—Rolling Bearing Model.” A general methodology for the accurate modeling of the nonlinear behavior of ball and roller bearings is proposed. A stiffness matrix is defined both for each rolling element and for the complete rolling bearing. Thus, it can be introduced into standard finite element models of complex mechanical systems, with the aim of predicting mechanical behavior and load and strain distributions. This method is applied to two cases of helicopter and automobile gearboxes. Deformable bearing rings considerably modify contact angle and load distribution, thus the coefficient values of the stiffness matrix are different from the classical values. The paper highlights how important it is to consider an overall model of the mechanical system rather than a local one in the vicinity of the bearings.

Analysis of tooth contact and load distribution of helical gears with crossed axes

This paper presents an approach for the analysis of tooth contact and load distribution of helical gears with crossed axis. The approach is based on a tooth contact model that accommodates the influence of tooth profile modifications, gear manufacturing errors and tooth surface deformation on gear mesh quality. In the approach the tooth contact load is assumed to be distributed along the tooth surface line that coincides with the relative principal direction of the contacting tooth surfaces. As compared with existing tooth contact (TCA) analysis model that assumes rigidity for the contacting surfaces, the model in this paper provides a more realistic analysis on gear transmission errors, contact patterns and the distribution of contact load. As a numerical example, the contact of a pair of helical gears with a small crossing angle is analyzed by the computer program that implements the approach. It is found from the analysis that helical gears with small crossing angles have meshing characteristics and load distribution similar to those of parallel-axis gears. The approach may be extended to other types of gearing.

Scattering of vertically-incident P-waves by an embedded pile

An exact theoretical formulation is presented for the analysis of a thin-walled pile embedded in an elastic half-space under vertically-incident P-wave excitation. In the framework of three-dimensional elastodynamics and a shell theory, the axisymmetrical wave-scattering problem is shown to be reducible to a set of Fredholm boundary integral equations. With the incorporation of the singular characteristics of the wave-induced contact load distributions into the solution scheme, a computational boundary element method is developed for a rigorous treatment of the seismic soil-structure interaction problem. Typical results for the dynamic contact load distributions, displacements, complex-valued foundation input motion functions, and resonant pile foundation response are included for direct engineering applications.

Effect of pitch distance, row spacing, end distance and bolt diameter on multi-fastened composite joints

Two-dimensional finite element modelling has been used to determine the contact stress and load distribution in a multi-fastened composite laminate plate forming the inner lap of a double-lap joi configuration subjected to tensile loading. The effect of both elastic and rigid outer laps was investigated. The results obtained for the former showed good agreement with previously published work. For a double row multi-fastened joint with rigid outer laps the effect of pitch distance, row spacing, end distance and pin diameter on the percentage of load transferred via the inboard and outboard rows was investigated. Friction at the interface was shown to exert a considerable effect on the local contact stress distribution around each hole. These results provide guidelines for the design of double row multi-fastened composite lap joints based on the optimum load transferred through the fasteners.

Mathematical boundary integral equation analysis of an embedded shell under dynamic excitations

AbstractA boundary integral equation method is presented for the analysis of a thin cylindrical shell embedded in an elastic half‐space under axisymmetric excitations. By virtue of a set of ring‐load Green's functions for the shell and a group of dynamic fundamental solutions for the semi‐infinite medium, the structure–medium interaction problem of wave propagation is shown to be reducible to a set of coupled boundary integral equations. Through the analysis of an auxiliary pair of Cauchy integral equations, the singularities of the contact stress distributions arc rendered explicit. With a direct incorporation of such analytical features into the formulation, an effective computational procedure is developed which involves an interpolation of regular functions only. Typical results for the dynamic contact load distributions, displacements, and complex compliance functions are included as illustrations. In addition to furnishing quantities of direct engineering interest, this treatment is apt to be useful as a foundation for further rigorous as well as approximate developments for various related physical problems and boundary integral methods.

Numerical Simulation of Piston Ring in Mixed Lubrication—A Nonaxisymmetrical Analysis

The assumption of axisymmetry, employed by most of studies on piston ring lubrication, probably gives a too idealistic model for the real situation. A theoretical model for a nonaxisymmetrical analysis of piston ring lubrication has been established in the present study. When a piston ring with an arbitrary free shape is fitted into the cylinder bore, the determination of ring deflection and contact load has been modeled mathematically as a Linear Complementary Problem (LCP). By combining LCP solution with lubrication analysis, the film thickness and contact load distribution over the circumference are obtained, leading to a more realistic simulation for piston ring lubrication. The friction force between piston ring and cylinder bore is predicted by the mixed lubrication model including the effects of surface roughness and asperity contact. The static distortion of cylinder bore, gas pressure variation, and lubricant starvation are also considered in the simulation. Results show that the contact pattern and film thickness between piston ring and cylinder bore are not exactly axisymmetrical. The main reason for the nonuniform contact is the asymmetry of ring elasticity, the static distortion and dynamic load created by the secondary movement of piston skirt.

Rational Mechanics of Axial Soil‐Pile Interaction

In the framework of three‐dimensional elastostatics and a higher‐order structural mechanics theory, an exact formulation is presented for the torsionless axisymmetric load‐transfer problem of a thin‐walled cylindrical pile of finite length embedded in a semi‐infinite medium. By virtue of a set of integral representations for the responses of the pile and the half‐space under arbitrary interfacial loads, the tangential and radial conditions of contact in the soil‐structure interaction problem are shown to be reducible to a system of Fredholm integral equations. Through an auxiliary analysis, the orders of the singularities of the contact load distributions can be determined mathematically. The results are incorporated into a numerical procedure for the solution of the Fredholm integral equations. Typical solutions for the contact load transfers, the internal axial force variation, and the displacement response as a function of various material and geometric parameters are included to illustrate the fundamental characteristics of the mechanical‐interaction problem.

Suspension Clamp and ACSR Electrical Conductor Contact Conditions

A one-dimensional model is presented for the analysis of contact between a typical suspension clamp and an overhead electrical conductor. Besides span parameters (sag angle, static tensile load), conductor curvature at the last point of contact is shown to depend on clamp profile. Strain measurements are performed on the bottom free surface of a typical commercially available suspension clamp, and of a simpler, yet similar, generic clamp, with a Bersimis ACSR conductor specimen. Various sag angle and tensile load combinations are imposed. Using an inverse method, measurements made on the generic clamp allow, through finite-element method modeling, the calculation of an approximate contact load distribution between clamp and conductor. With the usual assumption of minimum conductor bending stiffness, good agreement is found between experimental and theoretical results. Most notably, an experimentally observed tensile strain zone at the clamp bottom surface is shown to correlate well, both qualitatively and quantitatively, with a calculated localized contact region. Such tensile zone could be used to study contact conditions in other clamp-conductor systems.

Forced Torsional Oscillation From The Interior Of A Half-space

An analysis is presented of the torsional excitation of a rigid disc in bonded contact with the interior of an elastic half-space. With the aid of Hankel transforms, an exact formulation for the mixed boundary value problem is obtained as a pair of dual integral equations. After reduction of the dual integral equations to a Fredholm integral equation of the second kind, solutions to the problem are computed. Features of the problem, including a boundary-layer phenomenon, are illustrated through the results on the dynamic torque-rotation relationship, the stress field and the contact load distribution.

Effect of Isolated Talocalcaneal Fusion on Contact in the Ankle and Talonavicular Joints

A cadaveric model was developed to establish the articular contact area and load distribution in the ankle joint, posterior facet of the talocalcaneal joint, and talonavicular joint using pressure sensitive film. Positions of dorsiflexion, neutral, and plantarflexion were evaluated. This model was further used to determine the effect of talocalcaneal fusion on the articular contact area in the talonavicular and ankle joints. Alteration of articular contact was most pronounced in the talonavicular joint. There, a statistically significant reduction in contact area postfusion was noted when the foot was in the plantarflexed position. Reductions in ankle joint articular contact area were observed in the dorsiflexed and plantarflexed positions in the majority of specimens. Lateral displacement of the region of articular contact was noted in some specimens. A pressure-weighted centroid calculation was performed to provide a quantitative measure of the shift of the contact region.

Rocking rotation of a rigid disc in a half-space

An analysis is presented for the determination of the rotational response of a rigid circular disc embedded in a semi-infinite elastic medium under the action of a rocking moment. With the aid of Hankel transforms, a relaxed treatment of the mixed boundary value problem is formulated as dual integral equations. On reduction of the dual integral equations to a Fredholm integral equation which features a closed-form kernel, solutions to the inclusion problem are computed. In addition to providing a unified view of existing solutions for zero and infinite embedments, the present analysis reveals a severe boundary-layer phenomenon which is apt to be of significance to this class of problem in general. As illustrations, numerical results on the load-displacement relation and the response of the embedding medium, as well as the contact load distribution, are included.

On the axisymmetric interaction of a rigid disc with a semi-infinite solid

An analytical treatment is presented for the determination of the response of a vertically-loaded disc embedded in a semi-infinite elastic medium. By means of Love's method of potential and a set of relaxed boundary conditions, the mixed boundary value problem is formulated as dual integral equations with the aid of Hankel transforms. On the reduction of the dual integral equations to a Fredholm integral equation which features a closed-form kernel, solutions to the inclusion problem are computed. In addition to including existing solutions for zero and infinite embedment as degenerate cases, the present analysis reveals a severe boundary-layer phenomenon which is apt to be of significance to this class of problems in general. As illustrations, numerical results on the load-displacement relation, the response of the embedding medium, as well as the contact load distribution are included.

Effect of nut compliance on screw thread load distribution

A well-known theoretical equation for the distribution of contact load along threads in standard nut-bolt connections is generalized to incorporate the case of axially variable Young's moduli of the threaded elements. The influence of the material selection for homogeneous bolt and nut on the thread load concentration factor is initially addressed. The theoretical possibility of equalising the thread load distribution over the whole engagement by a convenient axial variation of the nut Young's modulus is then examined.

Contact load distribution along the length of a cylindrical shell

Contact load distribution along the length of a cylindrical shell

A three dimensional photoelastic study of the stress distributions in double helical epicyclic gears

This paper reports on part of a research programme which was carried out using two‐ and three‐dimensional photoelastic model techniques in order to analyse the stress distributions in a double‐helical epicyclic gear design incorporating typical features of production gear units.The paper describes the testing of two three‐dimensional models, one subjected to torque loading, i.e. tooth forces; the other to combined rotational and torque loading. Note is made of some of the problems inherent in the design and loading of complex models such as those used in the tests and of the solutions developed to overcome the difficulties.Attention is devoted to the analysis of contact loads and load distribution, maximum sub‐surface stresses, maximum root fillet bending stresses and the geometry of the lines of contact. General conclusions are drawn and an indication given of the subsequent extensive two‐dimensional test programme which was carried out.

The Effect of Misalignment on the Life of High Speed Cylindrical Roller Bearings

This paper describes an analytical investigation of the effects of misalignment and shaft speed on cylindrical roller bearing performance. Numerical results are presented for the contact load distributions and bearing fatigue lives under various amounts of misalignment for an NU308-type bearing operating under the load and speed conditions of a mainshaft bearing or a gearbox bearing in a helicopter gas turbine engine. The analysis is of use in bearing selection and in comparing different bearing designs for specific applications.