Faissal A. Moslehy

A model for friction in quasi-steady-state sliding part I. Derivation

Abstract This paper presents the derivation of a model for the prediction of the coefficient of friction for two elasto-plastic surfaces in quasi-steady-state sliding. A companion paper presents numerical results and a discussion on the implications of the models predictions in comparison with selected experimental data. The model considers the separate effects of asperity interaction and deformation, debris interaction and plowing, and adhesion, with partitioning of normal load (and contact areas) between different contacting elements. The analysis is restricted to nominally “steady state” sliding where the contact parameters are statistically invariant. The modifier “quasi” is used to emphasize that in tribodynamic systems there is no true equilibrium condition in which the frictional effects are “constant”.

Nondestructive detection of cavities by an inverse elastostatics boundary element method

Abstract The elastostatics boundary element method is applied in an inverse problem approach to the nondestructive detection of subsurface cavities in structures. The boundary conditions at the exposed surface are overspecified: tractions are specified and displacements are used as additional data for solving the inverse problem. In the developed iterative procedure, an initial guess is made for the shape of the cavity and a grid pattern is laid out. The use of this pattern allows one of the coordinates of the interior nodes to be fixed thus reducing the number of unknowns at each cavity node to one. The initial guess will not correspond to the actual cavity, consequently, the BEM solution will yield displacements which do not agree with the reference displacements. This leads to residuals at each node. The cavity is then located by iteratively driving these residuals to zero. Newtons method and the steepest descent method are considered in this effort. Iterative updates of the cavity geometry are kept within a physically realistic feasible region. Validation cases are presented for the detection of single circular and elliptic holes located at various positions within a rectangular plate. Numerical results demonstrate the successful detection of subsurface cavities by this method, Finally, results are presented for an experiment in which the surface displacements are determined by a laser speckle photography technique. A centrally located circular hole is successfully located using these surface displacement data.

A BEM based pattern search solution for a class of inverse elastostatic problems

A boundary element based solution, employing the Hooke-Jeeves pattern search method, is developed to determine internal cavity geometries in the inverse elastostatics problem. In contrast to existing methods which employ gradient based solutions, the developed method does not require gradient information, and consequently results in a simpler solution procedure. A boundary difference function (BDF) that provides a guide for the initial guess is introduced. The unknown cavity geometry is first assumed to be circular, and the algorithm is run until the general location of the cavity is determined. Subsequent refinement of the detected cavity geometry is affected using a periodic cubic spline discretization. Numerical results are presented to illustrate the effectiveness of the boundary difference function and to demonstrate the successful detection of the cavity. The effects of simulated experimental inputs with prescribed error are also presented.

Modeling friction and wear phenomena

Abstract This paper presents a modeling technique which can be applied to any tribosystem to simulate dynamic effects in unlubricated sliding. The model is based upon straightforward methods in the study of the dynamics of mechanical systems, and incorporates an interface comprised of asperities and debris. This interface transmits displacements and forces between the two sides of the mechanical system, both of which are explicitly included in the model. The dynamic parameters obtained include displacements and velocities at any points of interest, including the two reference planes constituting the contacting surfaces of the specimen and counterface. Through the interface model, fluctuations in the friction and normal forces also can be obtained, and are of more general interest to tribologists. By means of comparisons with experimental data from strain gage measurements, and by applying the methodology to two physically different machines, the modeling approach is validated. This paper describes the modeling approach, including excitation by means of asperity and debris interactions. Also included are representative results both from numerical and experimental studies.

Measurement of surface displacements in a tribological application

Laser-speckle photography is used to measure deformations which occur on the lateral surface of a rectangular-section pin which is in dry sliding contact against a counterface disk. The ‘side’ of the pin is illuminated by a pulsed ruby laser. A double-exposure specklegram is made to obtain deformations which occur between laser pulses. So, by appropriately sequencing pulses, deformation histories can be obtainedin situ.Since the exposed ‘side’ of the thin pin specimen represents the ‘cover’ layer under which subsurface sections lie, the deformation history observable through the laser-speckle method reflects the deformation behavior which is occurring on subsurface planes. The strain fields associated with the deformations are also calculated by the usual methods which include nonlinear terms (Lagrangian formulation). Moreover, this paper presents results obtained for the extent of the plastically deformed zone for different materials.These fundamental data, obtained by laser-speckle photography, yield direct displacement or strain histories for wear specimens. Such data are important for understanding wear phenomena, and for the development of engineering models for wear.

A boundary element method for stress reduction by optimal auxiliary holes

Stress concentration reduction in a plate with a hole is accomplished by introducing optimally sized and placed circular holes. This paper presents a method based on boundary elements and mathematical programming to determine these auxiliary holes. The mathematical programming method consists of a modified Newtons method and subsequent parallel tangents method (PARTAN). A solution is presented for an elliptical hole in a tension strip.

Mechanics of hip dysplasia reductions in infants using the Pavlik harness: A physics-based computational model

Biomechanical factors influencing the reduction of dislocated hips with the Pavlik harness in patients of Developmental Dysplasia of the Hip (DDH) were studied using a three-dimensional computer model simulating hip reduction dynamics in (1) subluxated and (2) fully dislocated hip joints. Five hip adductor muscles were identified as key mediators of DDH prognosis, and the non-dimensional force contribution of each in the direction necessary to achieve concentric hip reductions was determined. Results point to the adductor muscles as mediators of subluxated hip reductions, as their mechanical action is a function of the degree of hip dislocation. For subluxated hips in abduction and flexion, the Pectineus, Adductor Brevis, Adductor Longus, and proximal Adductor Magnus contribute positively to reduction, while the rest of the Adductor Magnus contributes negatively. In full dislocations all muscles contribute detrimentally to reduction, elucidating the need for traction to reduce Graf IV type dislocations. Reduction of dysplastic hips was found to occur in two distinct phases: (a) release phase and (b) reduction phase.

Inverse Boundary Element Solution for Locating Subsurface Cavities in Thermal and Elastostatic Problems

In a forward problem the system geometry, the governing equations, and the boundary and initial conditions are fully specified. The goal of solving such problem is to determine the dependent field variable, e.g., the temperature in a thermal problem and the stress or displacement field in a solid mechanics problem. In contrast, in an inverse problem either the system geometry, the governing equations, or the boundary and initial conditions are not fully specified, and the goal is to determine this unknown with the aid of some overspecified conditions. There are many such inverse problems which naturally arise in engineering and science. Surveys of inverse problem applications in heat transfer are given in [1,2], and applications to flaw detection and measuring residual stresses are found in [3–5].

Dynamic stiffness analysis in tribocontact

Abstract This paper presents the methodology and results of analysis for pin-on-disc tribosystems for the “dynamic stiffness” between specimen and counterface materials. Dynamic stiffness is defined in terms of the tendency of the contact between pin and disc to be maintained in the event that separation of the triboelements occurs. Thus both the dynamic stiffness and the more straightforwardly obtained static stiffness are important in the overall behavior of tribotesters since system response is increasingly recognized as an important factor in friction and wear. In the present work, two designs for application of normal load are investigated. One of these is the “dead-weight” technique; the other is essentially the “governor mechanism”. With the dead-weight design the normal load is applied to a rotating disc through a pivoted lever. With the governor, instead of controlling speed by means of displacement, the normal force applied to the rotating disc is established by controlling the speed of an independently driven motor. With both systems the rotating disc contacts a stationary pin. In order to analyze the dynamic interaction between pin and disc it is necessary to model the pin and its supports, as well as the disc and the mechanisms which are used to provide the normal load. These models are represented in terms of lumped parameters. For purposes of analysis and of comparison between the two alternative designs, the initial conditions consisted of a nominal separation between pin and disc, and a zero approach velocity. In tribotesting, such an event might occur with the removal of a relatively large piece of wear debris. While unlikely as such, this initial condition allows comparison between the two configurations. This comparison then determines the dynamic stiffness for the two designs. Interestingly, the governor mechanism provides excellent dynamic stiffness as well as tunable static stiffness. The latter may be useful in a general sense in that friction and/or wear test simulations may be made to resemble closely tribocontact stiffness conditions which occur in practice.

A patient-specific model of the biomechanics of hip reduction for neonatal Developmental Dysplasia of the Hip: Investigation of strategies for low to severe grades of Developmental Dysplasia of the Hip

A physics-based computational model of neonatal Developmental Dysplasia of the Hip (DDH) following treatment with the Pavlik Harness (PV) was developed to obtain muscle force contribution in order to elucidate biomechanical factors influencing the reduction of dislocated hips. Clinical observation suggests that reduction occurs in deep sleep involving passive muscle action. Consequently, a set of five (5) adductor muscles were identified as mediators of reduction using the PV. A Fung/Hill-type model was used to characterize muscle response. Four grades (1-4) of dislocation were considered, with one (1) being a low subluxation and four (4) a severe dislocation. A three-dimensional model of the pelvis-femur lower limb of a representative 10 week-old female was generated based on CT-scans with the aid of anthropomorphic scaling of anatomical landmarks. The model was calibrated to achieve equilibrium at 90° flexion and 80° abduction. The hip was computationally dislocated according to the grade under investigation, the femur was restrained to move in an envelope consistent with PV restraints, and the dynamic response under passive muscle action and the effect of gravity was resolved. Model results with an anteversion angle of 50° show successful reduction Grades 1-3, while Grade 4 failed to reduce with the PV. These results are consistent with a previous study based on a simplified anatomically-consistent synthetic model and clinical reports of very low success of the PV for Grade 4. However our model indicated that it is possible to achieve reduction of Grade 4 dislocation by hyperflexion and the resultant external rotation.