Effect Of Directionality Of Grinding Marks On Friction And Formation Of Transfer Layer

Surface texture influences friction and transfer layer formation during sliding. In the present investigation, basic studies were conducted using inclined pin-on-plate sliding tester to understand the effect of directionality of surface grinding marks of hard material on friction and transfer layer formation during sliding against soft materials. 080 M40 steel plates were ground to attain different surface roughness with unidirectional grinding marks. Then pins made of soft materials such as pure Al, pure Mg and Al-Mg alloy were slid against the prepared steel plates. Grinding angle (i.e., the angle between direction of sliding and grinding marks) was varied between 0 degrees and 90 degrees in the tests. Experiments were conducted under both dry and lubricated conditions on each plate in ambient environment. It was observed that the transfer layer formation and the coefficient of friction, which has two components adhesion and plowing - depend primarily on the directionality of grinding marks of the harder mating surface, and independent of surface roughness of the harder mating surface. For the case of pure Mg, stick-slip phenomenon was observed under dry condition for all grinding angles and it was absent upto 20 degrees grinding angles under lubricated condition. However, for the case of Al, it was observed only under lubricated conditions for angles exceeding 20 degrees. As regards the alloy, namely, Al-Mg alloy, it, was absent in both conditions. For the case of pure Mg and Al, it was observed that the amplitude of stick-slip motion primarily depends on plowing component of friction. The grinding angle effect on coefficient of friction was attributed to the variation of plowing component of friction with grinding angle.

Studies On Friction And Formation Of Transfer Layer In Hcp Metals

Surface texture plays an important role in the frictional behavior and transfer layer formation of contacting surfaces. In the present investigation, basic experiments were conducted using an inclined pin-on-plate sliding apparatus to better understand the role of surface texture on the coefficient of friction and the formation of a transfer layer. In the experiments, soft HCP materials such as pure Mg and pure Zn were used for the pins and a hardened 080 M40 steel was used for the plate. Two surface parameters of the steel plates—roughness and texture—were varied in tests that were conducted at a sliding speed of 2 mm/s in ambient conditions under both dry and lubricated conditions. The morphologies of the worn surfaces of the pins and the formation of the transfer layer on the counter surfaces were observed using a scanning electron microscope. In the experiments, the occurrence of stick-slip motion, the formation of a transfer layer, and the value of friction were recorded. With respect to the friction, both adhesion and plowing components were analyzed. Based on the experimental results, the effect of surface texture on the friction was attributed to differences in the amount of plowing. Both the plowing component of friction and the amplitude of stick-slip motion were determined to increase surface textures that promote plane strain conditions and decrease the textures that favor plane stress conditions.

Correlating The Features Of Topography To Friction By Sliding Experiments

Friction can influence the quality of the finished product to a large extent in certain manufacturing processes. Sheet metal forming is a particular case, where the friction between the hard-die and the relatively soft work-piece can be extremely important. Under such conditions, topography of the harder surface can influence the resistance to traction at the interface. This paper discusses about the correlation between certain features of the surface; topography and coefficient of friction based on experiments involving sliding of a few soft metal pins against a harder material. A brief description of the experimental procedure and the analysis are presented. A hybrid parameter which encapsulates both the amplitude features as well as the relative packing of peaks is shown to correlate well with the coefficient of friction.

Fatigue Laws Via Functional Equations

In routine industrial design, fatigue life estimation is largely based on S-N curves and ad hoc cycle counting algorithms used with Miner's rule for predicting life under complex loading. However, there are well known deficiencies of the conventional approach. Of the many cumulative damage rules that have been proposed, Manson's Double Linear Damage Rule (DLDR) has been the most successful. Here we follow up, through comparisons with experimental data from many sources, on a new approach to empirical fatigue life estimation (A Constructive Empirical Theory for Metal Fatigue Under Block Cyclic Loading', Proceedings of the Royal Society A, in press). The basic modeling approach is first described: it depends on enforcing mathematical consistency between predictions of simple empirical models that include indeterminate functional forms, and published fatigue data from handbooks. This consistency is enforced through setting up and (with luck) solving a functional equation with three independent variables and six unknown functions. The model, after eliminating or identifying various parameters, retains three fitted parameters; for the experimental data available, one of these may be set to zero. On comparison against data from several different sources, with two fitted parameters, we find that our model works about as well as the DLDR and much better than Miner's rule. We finally discuss some ways in which the model might be used, beyond the scope of the DLDR.

Axially Loaded Timoshenko Rotors From A Prestressed Continuum Approach

We consider an axially loaded Timoshenko rotor rotating at a constant speed and derive its governing equations from a continuum viewpoint. The primary aim of this paper is to understand the source and role of gyroscopic terms, when the rotor is viewed not as a Timoshenko beam but as a genuine 3D continuum. We offer the primary insight that macroscopically observed gyroscopic terms may also, quite equivalently, be viewed as external manifestations of internally existing spin-induced prestresses at the continuum level. To demonstrate this idea with an analytical example (the Timoshenko rotor), we have studied the reliable equations of Choi et al. (Journal of Vibration and Acoustics, 114, 1992, 249-259). Using a straightforward application of our insight in the framework of nonlinear elasticity, we obtain equations that exactly match Choi et al. for the case with no axial load. For the case of axial preload, our straightforward formulation leads to a slightly different set of equations that have negligible numerical consequence for solid rotors. However, we offer a macroscopic, intuitive, justification for modifying our formulation so as to obtain the exact equations of Choi et al. with the axial load included.

Infinite Dimensional Slow Modulations In A Delayed Model For Orthogonal Cutting Vibrations

We apply the method of multiple scales (MMS) to a well known model of regenerative cutting vibrations in the large delay regime. By ``large'' we mean the delay is much larger than the time scale of typical cutting tool oscillations. The MMS upto second order for such systems has been developed recently, and is applied here to study tool dynamics in the large delay regime. The second order analysis is found to be much more accurate than first order analysis. Numerical integration of the MMS slow flow is much faster than for the original equation, yet shows excellent accuracy. The main advantage of the present analysis is that infinite dimensional dynamics is retained in the slow flow, while the more usual center manifold reduction gives a planar phase space. Lower-dimensional dynamical features, such as Hopf bifurcations and families of periodic solutions, are also captured by the MMS. Finally, the strong sensitivity of the dynamics to small changes in parameter values is seen clearly.

A Global Constraint On Relative Rotation To Avoid Lumped Compliant Mechanisms In Topology Optimization

Some of the well known formulations for topology optimization of compliant mechanisms could lead to lumped compliant mechanisms. In lumped compliance, most of the elastic deformation in a mechanism occurs at few points, while rest of the mechanism remains more or less rigid. Such points are referred to as point-flexures. It has been noted in literature that high relative rotation is associated with point-flexures. In literature we also find a formulation of local constraint on relative rotations to avoid lumped compliance. However it is well known that a global constraint is easier to handle than a local constraint, by a numerical optimization algorithm. The current work presents a way of putting global constraint on relative rotations. This constraint is also simpler to implement since it uses linearized rotation at the center of finite-elements, to compute relative rotations. I show the results obtained by using this constraint oil the following benchmark problems - displacement inverter and gripper.

A Jacobian-Based Algorithm for Planning Attitude Maneuvers Using Forward and Reverse Rotations

Algorithms for planning quasistatic attitude maneuvers based on the Jacobian of the forward kinematic mapping of fully-reversed (FR) sequences of rotations are proposed in this paper. An FR sequence of rotations is a series of finite rotations that consists of initial rotations about the axes of a body-fixed coordinate frame and subsequent rotations that undo these initial rotations. Unlike the Jacobian of conventional systems such as a robot manipulator, the Jacobian of the system manipulated through FR rotations is a null matrix at the identity, which leads to a total breakdown of the traditional Jacobian formulation. Therefore, the Jacobian algorithm is reformulated and implemented so as to synthesize an FR sequence for a desired rotational displacement. The Jacobian-based algorithm presented in this paper identifies particular six-rotation FR sequences that synthesize desired orientations. We developed the single-step and the multiple-step Jacobian methods to accomplish a given task using six-rotation FR sequences. The single-step Jacobian method identifies a specific FR sequence for a given desired orientation and the multiple-step Jacobian algorithm synthesizes physically feasible FR rotations on an optimal path. A comparison with existing algorithms verifies the fast convergence ability of the Jacobian-based algorithm. Unlike closed-form solutions to the inverse kinematics problem, the Jacobian-based algorithm determines the most efficient FR sequence that yields a desired rotational displacement through a simple and inexpensive numerical calculation. The procedure presented here is useful for those motion planning problems wherein the Jacobian is singular or null.

Fatigue crack propagation analysis of plaque rupture

Rupture of atheromatous plaque is the major cause of stroke or heart attack. Considering that the cardiovascular system is a classic fatigue environment, plaque rupture was treated as a chronic fatigue crack growth process in this study. Fracture mechanics theory was introduced to describe the stress status at the crack tip and Paris' law was used to calculate the crack growth rate. The effect of anatomical variation of an idealized plaque cross-section model was investigated. The crack initiation was considered to be either at the maximum circumferential stress location or at any other possible locations around the lumen. Although the crack automatically initialized at the maximum circumferential stress location usually propagated faster than others, it was not necessarily the most critical location where the fatigue life reached its minimum. We found that the fatigue life was minimum for cracks initialized in the following three regions: the midcap zone, the shoulder zone, and the backside zone. The anatomical variation has a significant influence on the fatigue life. Either a decrease in cap thickness or an increase in lipid pool size resulted in a significant decrease in fatigue life. Comparing to the previously used stress analysis, this fatigue model provides some possible explanations of plaque rupture at a low stress level in a pulsatile cardiovascular environment, and the method proposed here may be useful for further investigation of the mechanism of plaque rupture based on in vivo patient data.

In vivo mri-based estimation of time-dependent elastic modulus in healthy arteries

The elastic properties of the arterial wall have been the subject of physiological, clinical and biomedical research for many years. There is convincing evidence that the elastic properties of the large arteries are seriously impaired in the presence of cardiovascular disease (CVD), due to alterations in the intrinsic structural and functional characteristics of vessels [1]. Early detection of changes in the elastic modulus of arteries would provide a powerful tool for both monitoring patients at high cardiovascular risk and testing the effects of pharmaceuticals aimed at stabilizing existing plaques by stiffening them or lowering the lipids.

Fluid-structure interaction study on human arterial plaque with patient specific geometry and boundary conditions

Atherosclerotic plaque rupture has been extensively considered as the leading cause of death in western countries. It is believed that high stresses within plaque can be an important factor on triggering the rupture of the plaque. Stress analysis in the coronary and carotid arteries with plaque have been developed by many researchers from 2D to 3-D models, from structure analysis only to the Fluid-Structure Interaction (FSI) models[1].

Stress analysis on human arterial plaques by fluid structure interactions - Multi-case study

Atherosclerotic plaque rupture has been extensively considered as the leading cause of death in the world. It is believed that high stress within plaque can be an important factor which can trigger the rupture of the plaque. High resolution multi-spectral magnetic resonance imaging (MRI) has allowed the plaque components (arterial wall, lipids, and fibrous cap) to be visualized in vivo [1]. The patient specific finite element model can be generated from the image data to perform stress analysis and provide critical information on understanding plaque rupture mechanisms [2]. The present work is to apply the procedure to a total of 14 patients (S1 ∼ S14), to study the stress distributions on carotid artery plaque reconstructed from multi-spectral magnetic resonance images, and the possible relationships between stress and plaque burdens.

Pulse-echo ultrasound transit time spectroscopy: A comparison of experimental measurements and simulation prediction

Considering ultrasound propagation through complex composite media as an array of parallel sonic rays, a comparison of computer simulated prediction with experimental data has previously been reported for transmission mode (where one transducer serves as transmitter, the other as receiver) in a series of ten acrylic step-wedge samples, immersed in water, exhibiting varying degrees of transit time inhomogeneity. In this study, the same samples were used but in pulse-echo mode, where the same ultrasound transducer served as both transmitter and receiver, detecting both ‘primary’ (internal sample interface) and ‘secondary’ (external sample interface) echoes. A transit time spectrum (TTS) was derived, describing the proportion of sonic rays with a particular transit time. A computer simulation was performed to predict the transit time and amplitude of various echoes created, and compared with experimental data. Applying an amplitude-tolerance analysis, 91.7±3.7% of the simulated data was within ±1 standard deviation (STD) of the experimentally measured amplitude-time data. Correlation of predicted and experimental transit time spectra provided coefficients of determination (R2) ranging from 100.0% to 96.8% for the various samples tested. The results acquired from this study provide good evidence for the concept of parallel sonic rays. Further, deconvolution of experimental input and output signals has been shown to provide an effective method to identify echoes otherwise lost due to phase cancellation. Potential applications of pulse-echo ultrasound transit time spectroscopy (PE-UTTS) include improvement of ultrasound image fidelity by improving spatial resolution and reducing phase interference artefacts.

Approximate closed-form solutions of realistic true proportional navigation guidance using the Adomian decomposition method

Approximate closed-form solutions of the non-linear relative equations of motion of an interceptor pursuing a target under the realistic true proportional navigation (RTPN) guidance law are derived using the Adomian decomposition method in this article. In the literature, no study has been reported on derivation of explicit time-series solutions in closed form of the nonlinear dynamic engagement equations under the RTPN guidance. The Adomian method provides an analytical approximation, requiring no linearization or direct integration of the non-linear terms. The complete derivation of the Adomian polynomials for the analysis of the dynamics of engagement under RTPN guidance is presented for deterministic ideal case, and non-ideal dynamics in the loop that comprises autopilot and actuator dynamics and target manoeuvre, as well as, for a stochastic case. Numerical results illustrate the applicability of the method.

Rotating Beams and Nonrotating Beams With Shared Eigenpair

In this paper, we look for rotating beams whose eigenpair (frequency and mode-shape) is the same as that of uniform nonrotating beams for a particular mode. It is found that, for any given mode, there exist flexural stiffness functions (FSFs) for which the jth mode eigenpair of a rotating beam, with uniform mass distribution, is identical to that of a corresponding nonrotating uniform beam with the same length and mass distribution. By putting the derived FSF in the finite element analysis of a rotating cantilever beam, the frequencies and mode-shapes of a nonrotating cantilever beam are obtained. For the first mode, a physically feasible equivalent rotating beam exists, but for higher modes, the flexural stiffness has internal singularities. Strategies for addressing the singularities in the FSF for finite element analysis are provided. The proposed functions can be used as test-functions for rotating beam codes and for targeted destiffening of rotating beams.