Elliptic Area Research Articles

Ellipse area calculations and their applicability in posturography

The quantification of postural sway is considered to be an essential part of posturography and is important for research and clinical utility. A widely used method to calculate the scatter of center of pressure data is an ellipse that encloses about 100(1−α)% of the observations. However, underlying definitions and terminologies have been misused in many cases. Hence, outcomes of different studies are proved to be incommensurable. In order to attain inter-study comparability, standardization of calculation methods has to be advanced. This work features a comprehensive and consistent overview of the methods for elliptic area approximation contrasting general principles of confidence and prediction regions. As a result, we recommend the usage of the prediction ellipse, as far as we demonstrate that confidence ellipses emerge to be inappropriate for posturographic scatter evaluation. Furthermore, we point at problems that come along with different sample sizes.

Approximate modelling of resulting dry friction forces and rolling resistance for elliptic contact shape

There are many examples of mechanical systems with non-point friction contacts (billiard ball, Thompson top, wobblestone, electric polishing machine, the wobblestone, the Celtic stone), where the assumption of one-dimensional dry friction model do not necessarily lead to satisfactory accuracy of the numerical simulation. Moreover the rolling resistance often plays an important role in such systems. The paper is devoted to the problem of developing an approximate coupled model of resulting dry friction force and moment as well as rolling resistance, suitable for fast numerical simulation of rigid bodies with friction contacts, i.e. allowing to avoid the space discretization. An integral model of dry friction components is built under assumption of classical Coulomb friction law and fully developed sliding on the contact area of general shape and arbitrary contact pressure distribution. Then the special model of stress distribution over the elliptic contact area is developed, being a kind of generalization of Hertzian normal stress distribution, with addition of special distortion related to the rolling resistance. Finally some original approximate models of friction force and moment are proposed, based on Pade approximants and their generalizations as well as in the form of piecewise polynomial functions.

Variations in seismic velocity and attenuation associated with seismogenesis: A numerical verification using ambient noise

Seismic velocity variations associated with the seismogenic process have been studied worldwide for almost half a century since the dilatancy hypothesis proposed in early 1970s. However, the reports in seismogenesis-associated variations in attenuation are rare. Reports on simultaneous variation of velocity and attenuation are even rarer. The conventional way to obtain the seismogenic temporal variation in velocity and attenuation is through the observation of travel time and amplitude variations of microseismicity in a seismogenic zone. Anyhow, for some major earthquakes there may not always be microseismicity prior to the mainshock. Thus, obtaining a complete record of seismic velocity and attenuation variation from microseismicity is severely limited if pre-mainshock microseismicity exists. In contrast, seismic ambient noise is an ideal source for crustal stimulation for monitoring temporal variations in velocity and attenuation in a seismogenic zone.In this paper the seismogenesis-associated seismic velocity and attenuation variations shown as some observable parameters in ambient noise measurements are verified using a numerical simulation approach. First, based on the temporal variation in seismic velocity observed along the Longmenshan fault associated with the 2008 Wenchuan earthquake, we divided the seismogenic process into six phases upon velocity drop stages in an elliptic area in the crust. Second, using finite difference time domain method we generated 30-minute low frequency ambient noise over a vertical profile of 200×45km and recorded it with a 90-station array on the surface. Next, we processed the synthetic ambient noise records to get the auto-correlation function (ACF), cross-correlation function (CCF), Rayleigh wave dispersion curve, and horizontal-to-vertical spectral ratio (H/V). Finally, we examined the temporal variation of these parameters versus the phases of the seismogenic process and found the most pronounced changes occur in the phase with the largest velocity drop and the recovery phase directly before the mainshock.

Wear analysis of the offset type preloaded ball–screw operating at high speed

In a high-speed ball–screw transmission system, a preload is always applied in the ball–screw to avoid vibration and backlash during all linear transmission periods. However, the sliding wear is the main reason why the applied preload decreases or vanishes. This study presents a new two body abrasion model combining the kinematic theory describing the variations in the axial wear depths with the operating strokes, which is related to the preload directly. The contact shape of the contact asperities is considered to be an elliptic area with a different ellipticity ratio to simulate the grinding trace of a raceway. The total wear depth of the axis direction is dominated by the wear depth of an asperity, the contact ratio between the plastic and normal contact areas, and the wear frequency due to the relative speed of the two contact surfaces. The axial wear depth increases with a raising operating stroke, an increasing rotational speed, and a small ellipticity ratio for the contact shape. Analysis of the results indicates that a high ellipticity ratio of contacting asperities on a raceway can effectively reduce the increasing rate of wear in an offset type preloaded ball–screw when operating in a high rotational speed.

Detection of 90Y Extravasation by Bremsstrahlung Imaging for Patients Undergoing 90Y-Ibritumomab Tiuxetan Therapy

Extravasation of therapeutic (90)Y-ibritumomab tiuxetan can cause significant injury. Detection of extravasated (90)Y using a γ-camera for patients undergoing (90)Y-ibritumomab tiuxetan therapy is a challenge because of the inherently low efficiency of bremsstrahlung imaging and the interference of prompt and scattered photons from (111)In that are still present in the body at the time of (90)Y injection. We have configured a γ-camera to image bremsstrahlung radiation from superficial (90)Y in the presence of (111)In and evaluated the effectiveness using phantoms. Phantoms were constructed to contain (90)Y and (111)In with activity levels and with a geometry approximating conditions in a patient being scanned for evaluation of possible extravasation in the antecubital fossa. Imaging was performed using a camera equipped with medium-energy general-purpose (MEGP) and high-energy general-purpose (HEGP) collimators. The contrast that developed between the patch representing extravasated solution and the background was comparable for MEGP and HEGP collimators. With MEGP collimators and 5-min acquisitions, a patch containing 8.3 MBq (220 μCi) distributed over an elliptic area of 7 × 11 cm was clearly discernable. With our experimental arrangement, the lower limit of detection is approximately 8 MBq. We calculate that an extravasation of this much (90)Y would result in an absorbed dose to the skin and subcutaneous tissue of 2.5 Gy, which is close to the threshold for skin damage. This technique is therefore sensitive enough to be of use in the clinic when extravasation of (90)Y is suspected.

Implementation of the Contensou–Erismann tangent forces model in the Hertz contact problem

In frame of the Hertz contact problem, an approximate model to compute resulting wrench of the dry friction tangent forces is built up. The wrench consists of the total friction force and the drilling friction torque. An approach under consideration develops in a natural way the contact model constructed earlier. The dry friction force and torque are integrated over the contact elliptic area. Generally, an analytic computation of the integrals mentioned leads to the cumbersome calculation, tens of terms, including rational functions depending in turn on complete elliptic integrals. To implement the elastic bodies contact interaction computer model fast enough, one builds up an approximate model in the way initially proposed by Contensou.

Numerical Simulation of Myanmar Cyclone Nargis and the Associated Storm Surge Part II: Ensemble Prediction

A mesoscale ensemble prediction system (EPS) employing the Japan Meteorological Agency’s (JMA’s) high-resolution global analysis and forecast for initial and boundary conditions of the control run and perturbations from JMA’s one-week global EPS for initial and boundary perturbations is developed and applied to numerical simulations of cyclone Nargis. Using the JMA nonhydrostatic model (NHM) with a horizontal resolution of 10 km, the system reproduces Nargis’ development and the associated storm surge in southwestern Myanmar with plausible ensemble spreads.In the ensemble prediction with initial boundary perturbations, predicted positions of cyclone centers are distributed in an elliptic area whose major axis is oriented east-northeast, suggesting that track forecast errors tend to increase in the moving direction of Nargis. The location of the minimum surface pressure of the ensemble mean is closer to the best track than the control run, and root mean square errors (RMSEs) of the ensemble mean against analyses are smaller than those of the control run in all forecast variables. However, ensemble spreads tend to decrease in the latter half of the forecast period, and the cyclone center does not disperse enough compared with the track forecast error without the lateral boundary perturbation.When lateral boundary perturbations are implemented in addition to the initial perturbations, dispersion of the cyclone center and spread of the center pressure increase by about 50% at forecast time (FT) ¼ 42. The location of the minimum surface pressure in the ensemble mean shifts westward, reducing the track error. RMSEs of ensemble means become smaller than the ensemble prediction without lateral boundary perturbations.Ensemble forecasts of storm surge were conducted using the Princeton Ocean Model (POM). When surface wind and sea level pressure from JMA’s global EPS were input, the maximum surge was no more than 0.6 m even in the highest ensemble member. The POM simulation driven by the mesoscale ensemble prediction with NHM predicted a storm surge near 4 m in southwestern Myanmar, where the timings of the peak surge were dispersed widely from FT ¼ 33 to FT ¼ 56. When the ensemble mean was input to POM, the maximum surge was 1.5 m, despite the better accuracy of the ensemble mean in terms of RMSE. This result shows that the scenario is more important than the ensemble mean when applying the mesoscale ensemble prediction to disaster prevention.

Three-dimensional contact problems with friction for a composite elastic wedge

Contact problems for a composite elastic wedge in the form of two joined wedge-shaped layers with different aperture angles joined by a sliding clamp, where the layer under the punch is incompressible, are studied in a three-dimensional formulation. Conditions for a sliding or rigid clamp or the absence of stresses are set up on one face of the composite wedge. The integral equations of the problems are derived taking account of the friction forces perpendicular to the edge of the wedge. The method of non-linear boundary integral equations of the Hammerstein type is used when the contact area is unknown. A regular asymptotic solution is constructed for an elliptic contact area. By virtue of the incompressibility of the material of the layer in contact with the punch, this solution retains the well known root singularity in the boundary of the contact area when account is taken of friction.

Comparison of Small and Large Scale Wheel Tracking Devices

ABSTRACT This paper presents a comparison of results from two wheel tracking devices. It is part of a larger on-going collaborative research project between the University of Nottingham in the UK, Delft University of Technology in The Netherlands and LCPC in France on the development and Finite Element (FE) implementation of a non-linear elasto-visco-plastic constitutive model for asphalt. Two devices, a large scale and small scale device, encompassed by the European Standard and the former British Standard were used. Rutting evaluation at the same temperature, on two different materials for pavement surface layers was tested under the same conditions allowing the evaluation of the rutting rate to be determined which was found to be very close from one test to another but sensitive to mixture type. In addition to rutting results, the contact dimensions and pressures from the two devices are evaluated in both the static case and during motion using a flat force transducer on the surface of the slab. The stresses induced in the slabs were calculated using finite element simulations and the measured contact conditions. For different pressure distributions under the wheel the isotropic and deviatoric stresses at the centre of the slab were compared which showed the importance of a good understanding of the wheel/slab contact conditions. The paper provides experimental rutting results obtained at the same temperatures for two characteristic materials on two devices. For future mechanical modelling the wheel print was found to be smaller during the motion than static prints. For wheels using inflated tyres a constant pressure over and elliptic area was found to be appropriate. For hard rubber wheels a rectangular area with an elliptic pressure distribution is more realistic.

The dynamic wheel–rail contact stresses for wagon on various tracks

The maximal stress and tangential surface forces at the wheel–rail contact elliptic area are affected by the wheel–rail contact dynamic load and creepages. Dynamic wheel load is related to the wagon dynamic system, track and wheel–rail interaction. Creepages are related to the motion of wheelset and wheel–rail contact parameters. The paper presents an analysis of the effects of creepages on wheel–rail contact forces. A complete Australia wagon with three-piece bogies was modelled and various tracks were selected for the simulation of dynamic wheel–rail contact stresses. The results show that the maximal normal wheel–rail contact stresses is under 1600 MPa in a range of conditions of typical normal operation.

Impact of non-elliptic contact modelling in wheel wear simulation

Advances in simulation of railway wheel wear in the sense of material removal have drawn the attention to the importance of wheel–rail contact modelling. As a further step of enhancing the used simulation procedure in direction of increased generality and reduced need for application-dependent calibration, the focus of this investigation is the influence of non-elliptic contact models on the wheel wear rate and profile shape. To facilitate evaluation the semi-Hertzian contact procedure Stripes, developed by INRETS in France, has been implemented. To investigate the capabilities of Stripes to assess the contact area and pressure, shape comparisons have been made with other numerical methods for a set of wheel–rail contact situations. The referenced results are based on the linear elastic half-space assumption, elastic finite element analysis, and elastic–plastic finite element analysis. For reference also the elliptic contact area according to Hertz is shown as given by the contact data table of the multi-body simulation code. After exploring the properties of the Stripes procedure with respect to contact area estimation and pressure distribution, the focus is moved to the influence on wear rate, being the principal objective of this investigation. First the wear distribution over the contact patch is studied and compared to results using the elliptic model from the MBS code Gensys and the non-elliptic approach with Kalker's code Contact. Finally the evolution of the wheel profile is simulated for a few typical cases. This investigation of wear distributions over non-elliptic patches under different operating conditions indicates significant differences compared to both Contact and the applied Hertzian approach. The expansion from single contact occasions to complete simulations indicates comparable material removal rates but relocation towards the flange side. This tendency is apparent in all of the cases shown, however limited to initial wear in tangent run or reasonably mild curve negotiation.

Improvement of posture stability by vibratory stimulation following anterior cruciate ligament reconstruction

Surgical reconstruction of the anterior cruciate ligament (ACL) may reduce, but it does not always eliminate, knee and body instability because of a persisting proprioceptive deficit. In order to enhance body stability, a new protocol of treatment has been proposed consisting of mechanical vibration (100 Hz frequency and < 20 microm amplitude) of the quadriceps muscle in the leg that has undergone ACL reconstruction. In our trials, stimulation was performed when the quadriceps muscle was kept isometrically contracted. Treatment was started one month after surgery. Vibration was applied for short periods over three consecutive days. Nine months after treatment, postural stability was re-evaluated with the subjects standing on one leg with open and with closed eyes. The postural stability of the subjects having undergone vibration treatment, standing on the operated leg was significantly improved one day after treatment when evaluated as mean of speed and elliptic area of the center of pressure. The improvement persisted and increased during the following weeks. Peak torques of the operated leg extensor muscles also increased and reached values close to that of the leg, which had not been operated. Conversely, the balance of the untreated subjects standing on the operated leg did not improve and the restoration of the extensor muscle peak torque was poor. It is concluded that short lasting proprioceptive activation by vibration may lead to a faster and more complete equilibrium recovery probably by permanently changing the network controlling knee posture.

Shakedown analyses for rolling and sliding contact problems

There is a range of problems where repeated rolling and sliding contact occurs over a half space of an elastic–perfectly plastic material. For such problems shakedown and limit analysis provide significant advantages over other forms of analysis when a global understanding of deformation behaviour is required. In this paper, a recently developed numerical upper bound method, the Linear Matching Method (LMM), for shakedown analyses is applied to the solution of a problem previously considered by Ponter et al. [Ponter, A.R.S., Hearle, A.D., Johnson, K.L., 1985. J. Mech. Phys. Solids 33 (4), 339–362] for a moving Hertzian contact, with sliding friction. This semi-analytic solution is an upper bound based on certain specific kinematic assumptions. We show that the Ponter, Hearle and Johnson solution is a reasonable approximate solution for a circular contact area but is less accurate for an elliptic contact area. For an elliptic contact area LLM solutions converge to the line contact solution. The effect of the non-coincidence of the direction of travel and slide is also investigated.

Enhanced distance-based location management of mobile communication systems using a cell coordinates approach

In managing the locations of mobile users in mobile communication systems, the distance-based strategy has been proven to have better performance than other dynamic strategies, but is difficult to implement. A simple approach is introduced to implement the distance-based strategy by using the cell coordinates in calculating the physical distance traveled. This approach has the advantages of being independent of the size, shape, and distribution of cells, as well as catering for the direction of movement in addition to the speed of each mobile terminal. An enhanced distance-based location management strategy is proposed to dynamically adjust the size and shape of location area for each individual mobile terminal according to the current speed and direction of movement. It can reduce the location management signaling traffic of the distance-based strategy by half when mobile terminals have predictable directions of movement. Three types of location updating schemes are discussed, namely, Circular Location Area, Optimal Location Area, and Elliptic Location Area. Paging schemes using searching techniques such as expanding distance search based on the last reported location and based on the predicted location, and expanding direction search are also explored to further reduce paging signal traffic by partitioning location areas into paging areas.

Evaluation of subsurface contact stresses in railroad wheels using an elastic half-space model

Railroad wheels fail in two main modes: rolling surface defects like spalling, shelling and wear, and internal defects including cracks propagating after a change takes place in the original stress pattern. Although the effects of the latter are almost always catastrophic, the former is more usual. The onset of rolling surface defects depends on the strength of the surface and the applied loads. The strength is related to surface hardness and can be determined through experimental evaluation under controlled conditions. Evaluating the loads is one of the challenges for contact researchers. This paper presents the evaluation of the stress field inside elastic rolling bodies with an elliptic area of contact. This kind of model can be applied to wheel-rail contact phenomena. Typical high freight transportation loads are used in conjunction with regular recommended wheel and rail sizes. The results have shown that shear stress reaches the maximum magnitude below the surface of contact, and this explains the presence of shelling defects in service. They have also shown that a new model including plasticity is required, because the range of the stresses reached surpasses, by far, the elastic limit

A personal identity annotation overlay system using a wearable computer for augmented reality

There is surely no doubt that computers play an important role in our life. The use of computers ranges from convenient tools like calculators to various lives saving equipment. They help to save a great amount of human effort in many areas. To accomplish special tasks in different workplaces, it would be of great advantage to develop proper devices and to use wearable computers to meet the goals successfully. That is why we use the support of different kinds of computers such as the Global Positioning System (GPS), personal digital assistant (PDA), digital bar code reader, etc. Using a portable or wearable computer, we can work outside our offices or even in bed. Thus, our work environment has changed considerably. In many new environments, computers can help us to increase our perception and interaction abilities. Augmented reality (AR) is a good example of a tool used to enhance a human's perception and interaction abilities. AR provides a natural method for presenting computer-generated information by overlaying graphics into a view of the real world. This paper describes a personal identity annotation system using a wearable computer for an AR environment, which allows its user to recognize unknown persons. For implementing, the proposed system uses skin-color pixels coupled with shape and face features to detect and track faces in images taken by a wearable camera. Faces in a view are detected by searching for connected regions of skin color pixels. For each region big enough, an elliptic area is determined with the highest image gradient magnitude around the perimeter and the highest number of enclosed skin color pixels. The face regions enclosed by the determined ellipses are then used by the system to recognize multiple faces based on the face similarity. Experimental results show that the proposed system has both quality and performance to be used as a guiding system for visitors in various equipments.

Dust Generation Properties of Solid Lubricant Film Coated and Perfluoropolyether Lubricated Ball Bearings

The purpose of this work is to elucidate the properties of ball bearings used for clean applications. Dust, namely wear debris particle generation behavior of ball bearings lubricated with solid lubricant films and low vapor pressure PFPE (perfluoropolyether) grease was investigated using a laser scattering type dust counter under small-angle oscillatory conditions. In the case of the solid lubricated bearing, dust generation began to increase rapidly at a certain number of oscillatory cycles, as deduced from the bearing surface damage. Bearings lubricated with a MoS2/Ag layer and MoS2 sputtered films showed less dust generation, starting torque and surface damage than ion-plated Ag and Au film lubricated and unlubricated bearings. Dust generation was deduced to be due to the damage formation of oscillatory ball bearings, based on the size of the contact elliptic area. The total number of particles generated from the ball bearing lubricated with PFPE grease is very large, but bearing damage is very small. Degraded PFPE was observed on the side plate seal by FTIR. Therefore, dust generation from a PFPE-lubricated bearing is deduced to be due to PFPE degradation. Particles generated from bearings with dry contact include large particles. In contrast, most of the particles generated from bearings lubricated with PFPE grease are very small. Side plate seals of ball bearings decrease the amount of dust generated from these bearings. [S0742-4787(00)00704-9]

Surgical correction of overriding fifth toe using the Ruiz-Mora procedure

Correction of an overriding fifth toe. Fixed, painful overriding fifth toe without symptoms over the fifth metatarsal head. Peripheral vascular diseases. Soft tissue defects or infection. Pain over head of fifth metatarsal. Flexible deformity. Excision of proximal phalanx of fifth toe after excision of an elliptic skin area through a plantar approach. Correction of malposition during skin closure (dermodesis). Between 1986 and 1997, 24 Ruiz-Mora procedures were done in 20 patients (average age 38 years). Average length of follow-up: 6.6 (1 to 11) years. All patients were satisfied with the result. Two patients complained about the marked shortening of the fifth toe and skin problems caused by it. In 5 patients a hammer toe deformity of the fourth toe developed postoperatively, in 2 patients a symptomless floppy toe developed. Using the Kitaoka score an excellent result was obtained 8 times, a good result 12 times and satisfactory 4 times. No poor result was seen.

Asymptotic solution of the problem of the pressure of a rigid body on a membrane

The problem of the pressure on a membrane of a punch in the form of an elliptic paraboloid is investigated assuming that the contact area is small. By means of the method of matched asymptotic expansions, the problem of unilateral contact is developed for an inner asymptotic expansion, the solution of which is based on results for the case of an infinite membrane [1]. The influence of the boundary of the membrane is modelled in formulating the asymptotic conditions at infinity. The relation between the force impressing the punch and its motion is determined. The sensitivity of the parameters of the elliptic contact area to the dimensions of the membrane and the position of the centre of the punch is investigated. A refined asymptotic model of contact interaction is proposed.

Study on Load Carrying Characteristics of Crossed Helical Gears (Special Focus on Scuffing Strength, Wear and Friction Loss)

Crossed helical gears fail mainly by scuffing. Power transmission is low, because the Hertzian pressure in the small elliptic contact area is very high, and the sliding velocity between two contacting tooth surfaces is very high compared with other kind of gears. However, crossed helical gears have important advantages, since they are easy to produce and their engagement is not influenced by mounting errors in center distance or shaft angle. This study presents some new ways of improving the load carrying capacity of crossed helical gears. The influence of lubricating oil, tooth surface treatment, and tooth form on the limiting load for scuffing was studied experimentally. The results were summarized and formulas were established in view of practical design.