The rolling ball problem on the plane revisited

By a sequence of rollings without slipping or twisting along segments of a straight line of the plane, a spherical ball of unit radius has to be transferred from an initial state to an arbitrary final state taking into account the orientation of the ball. We provide a new proof that with at most 3 moves, we can go from a given initial state to an arbitrary final state. The first proof of this result is due to Hammersley ( 1983). His proof is more algebraic than ours which is more geometric. We also showed that generically no one of the three moves, in any elimination of the spin discrepancy, may have length equal to an integral multiple of 2 pi.

Dominant-non-dominant asymmetry of kicking a stationary and rolling ball in a futsal context

The aim of this study was to analyse the characteristics of the asymmetries in the dominant and non-dominant limbs when kicking stationary and rolling balls. Ten experienced Brazilian amateur futsal players participated in this study. Each participant performed kicks under two conditions (stationary ball vs. rolling ball) with the dominant and non-dominant limbs (five kicks per condition per limb). We analysed the kicking accuracy, ball and foot velocities, angular joint displacement and velocity. The asymmetry between the dominant and non-dominant limbs was analysed by symmetry index and two-way repeated measures ANOVA. The results did not reveal any interaction between the condition and limb for ball velocity, foot velocity and accuracy. However, kicking with the dominant limb in both kicks showed higher ball velocity (stationary ball: dominant - 24.27 ± 2.21 m · s(-1) and non-dominant - 21.62 ± 2.26 m · s(-1); rolling ball: dominant - 23.88 ± 2.71 m · s(-1) and non-dominant - 21.42 ± 2.25 m · s(-1)), foot velocity (stationary ball: dominant - 17.61 ± 1.87 m · s(-1) and non-dominant - 15.58 ± 2.69 m · s(-1); rolling ball: dominant - 17.25 ± 2.26 m · s(-1) and non-dominant - 14.77 ± 2.35 m · s(-1)) and accuracy (stationary ball: dominant - 1.17 ± 0.84 m and non-dominant - 1.56 ± 1.30 m; rolling ball: dominant - 1.31 ± 0.91 m and non-dominant - 1.97 ± 1.44 m). In addition, the angular joint adjustments were dependent on the limb in both kicks (the kicks with non-dominant limb showed lower hip external rotation than the kicks with the dominant limb), indicating that the hip joint is important in kick performance. In conclusion, the kicks with the non-dominant limb showed different angular adjustments in comparison to kicks with the dominant limb. In addition, kicking a rolling ball with the non-dominant limb showed higher asymmetry for accuracy, indicating that complex kicks are more asymmetric.

Performance comparisons of the kicking of stationary and rolling balls in a futsal context

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Aktionenlernen mit Selbstorganisierenden Karten und Reinforcement Learning

Die vorliegende Arbeit beschäftigt sich mit der Entwicklung eines Funktionsapproximators und dessen Verwendung in Verfahren zum Lernen von diskreten und kontinuierlichen Aktionen: 1. Ein allgemeiner Funktionsapproximator – Locally Weighted Interpolating Growing Neural Gas (LWIGNG) – wird auf Basis eines Wachsenden Neuralen Gases (GNG) entwickelt. Die topologische Nachbarschaft in der Neuronenstruktur wird verwendet, um zwischen benachbarten Neuronen zu interpolieren und durch lokale Gewichtung die Approximation zu berechnen. Die Leistungsfähigkeit des Ansatzes, insbesondere in Hinsicht auf sich verändernde Zielfunktionen und sich verändernde Eingabeverteilungen, wird in verschiedenen Experimenten unter Beweis gestellt. 2. Zum Lernen diskreter Aktionen wird das LWIGNG-Verfahren mit Q-Learning zur Q-LWIGNG-Methode verbunden. Dafür muss der zugrunde liegende GNG-Algorithmus abgeändert werden, da die Eingabedaten beim Aktionenlernen eine bestimmte Reihenfolge haben. Q-LWIGNG erzielt sehr gute Ergebnisse beim Stabbalance- und beim Mountain-Car-Problem und gute Ergebnisse beim Acrobot-Problem. 3. Zum Lernen kontinuierlicher Aktionen wird ein REINFORCE-Algorithmus mit LWIGNG zur ReinforceGNG-Methode verbunden. Dabei wird eine Actor-Critic-Architektur eingesetzt, um aus zeitverzögerten Belohnungen zu lernen. LWIGNG approximiert sowohl die Zustands-Wertefunktion als auch die Politik, die in Form von situationsabhängigen Parametern einer Normalverteilung repräsentiert wird. ReinforceGNG wird erfolgreich zum Lernen von Bewegungen für einen simulierten 2-rädrigen Roboter eingesetzt, der einen rollenden Ball unter bestimmten Bedingungen abfangen soll.

Friction coefficient and abrasive wear modes in ball-cratering tests conducted at constant normal force and constant pressure-Preliminary results

The micro-scale abrasive wear test by rotative ball has gained large acceptance in universities and research centers, being widely used in studies on the abrasive wear of materials. Two wear modes are usually observed in this type of test: ""rolling abrasion"" results when the abrasive particles roll on the surface of the tested specimen, while ""grooving abrasion"" is observed when the abrasive particles slide; the type of wear mode has a significant effect on the overall behaviour of a tribological system. Several works on the friction coefficient during abrasive wear tests are available in the literature, but only a few were dedicated to the friction coefficient in micro-abrasive wear tests conducted with rotating ball. Additionally, recent works have identified that results may also be affected by the change in contact pressure that occurs when tests are conducted with constant applied force. Thus, the purpose of this work is to study the relationship between friction coefficient and abrasive wear modes in ball-cratering wear tests conducted at ""constant normal force"" and ""constant pressure"". Micro-scale abrasive wear tests were conducted with a ball of AISI52100 steel and a specimen of AISIH10 tool steel. The abrasive slurry was prepared with black silicon carbide (SiC) particles (average particle size of 3 mu m) and distilled water. Two constant normal force values and two constant pressure values were selected for the tests. The tangential and normal loads were monitored throughout the tests and their ratio was calculated to provide an indication of the friction coefficient. In all cases, optical microscopy analysis of the worn craters revelated only the presence of grooving abrasion. However, a more detailed analysis conducted by SEM has indicated that different degrees of rolling abrasion have also occurred along the grooves. The results have also shown that: (i) for the selected values of constant normal force and constant pressure, the friction coefficient presents, approximately, the same range of values and (ii) loading conditions play an important role on the occurrence of rolling abrasion or grooving abrasion and, consequently, on the average value and scatter of the friction coefficient in micro-abrasive wear tests. (C) 2009 Elsevier B.V. All rights reserved.

Influence of grease rheology on thrust ball bearings friction torque

The friction torque and the operating temperatures in a thrust ball bearing were measured for seven different types of greases, including three biodegradable greases having low toxicity. These friction torque tests were performed using a modified Four-Ball machine. Rheological evaluations of the lubricating greases were made using a rheometer. Bleed oils were extracted from the greases and the dynamic viscosities were measured. In order to compare the performance of the lubricant greases in terms of friction, the grease characteristics were related to experimental results, showing that the interaction between thickener and base oil have strong influences in the bearing friction torque.

Experimental measuring procedure for the friction torque in rolling bearings

The reduction of the power loss generated in mechanical transmissions and the use of low friction biodegradable lubricants has been attracting considerable attention in recent times. Therefore, it is necessary to develop methods to test and evaluate the performance of such lubricants and compare them with conventional ones. In this sense, a Four-Ball Machine was modified allowing the test of rolling bearings. A 51107 thrust ball bearing was used to test two different greases and the corresponding base oils. Friction torque and operating temperatures were continuously monitored to quantify the power loss and the heat evacuation for each lubricant tested. Copyright © 2010 John Wiley & Sons, Ltd.

Friction torque in grease lubricated thrust ball bearings

Thrust ball bearings lubricated with several different greases were tested on a modified Four-Ball Machine, where the Four-Ball arrangement was replaced by a bearing assembly. The friction torque and operating temperatures in a thrust ball bearing were measured during the tests. At the end of each test a grease sample was analyzed through ferrographic techniques in order to quantify and evaluate bearing wear. A rolling bearing friction torque model was used and the coefficient of friction in full film lubrication was determined for each grease, depending on the operating conditions. The experimental results obtained showed that grease formulation had a very significant influence on friction torque and operating temperature. The friction torque depends on the viscosity of the grease base oil, on its nature (mineral, ester, PAO, etc.), on the coefficient of friction in full film conditions, but also on the interaction between grease thickener and base oil, which affected contact replenishment and contact starvation, and thus influenced the friction torque.

Vibration and oil analysis for monitoring problems related to water contamination in rolling

Trying to reduce particle contamination in lubrication systems, industries of the whole world spend millions of dollars each year on the improvement of filtration technology. In this context, by controlling fluid cleanliness, some companies are able to reduce failures rates up to 85 percent. However, in some industries and environments, water is a contaminant more frequently encountered than solid particles, and it is often seen as the primary cause of component failure. Only one percent of water in oil is enough to reduce life expectancy of a journal bearing by 80 percent. For rolling bearing elements, the situation is worse because water destroys the oil film and, under the extreme temperatures and pressures generated in the load zone of a rolling bearing element, free and emulsified water can result in instantaneous flash-vaporization giving origin to erosive wear. This work studies the effect of water as lubricant contaminant in ball bearings, which simulates a situation that could actually occur in real systems. In a designed bench test, three basic lubricants of different viscosities were contaminated with different contents of water. The results regarding oil and vibration analysis are presented for different bearing speeds.

Endurance tests of rolling contact bearings of conventional and high temperature steels under conditions simulating aircraft gas turbine applications

"Propulsion Laboratory, Contract no. AF 33(600)-22860, Task 3066-30233."

Flux Pinning Optimization of MgB(2) Bulk Samples Prepared Using High-Energy Ball Milling and Addition of TaB(2)

MgB(2) is considered to be an important conductor for applications. Optimizing flux pinning in these conductors can improve their critical currents. Doping can influence flux pinning efficiency and grain connectivity, and also affect the resistivity, upper critical field and critical temperature. This study was designed to attempt the doping of MgB(2) on the Mg sites with metal-diborides using high-energy ball milling. MgB(2) samples were prepared by milling pre-reacted MgB(2) and TaB(2) powders using a Spex 8000M mill with WC jars and balls in a nitrogen-filled glove box. The mixing concentration in (Mg(1-x)Ta(x))B(2) was up to x = 0.10. Samples were removed from the WC jars after milling times up to 4000 minutes and formed into pellets using cold isostatic pressing. The pellets were heat treated in a hot isostatic press (HIP) at 1000 degrees C under a pressure of 30 kpsi for 24 hours. The influence that milling time and TaB(2) addition had on the microstructure and the resulting superconducting properties of TaB(2)-added MgB(2) is discussed. Improvement J(c) of at high magnetic fields and of pinning could be obtained in milled samples with added TaB(2) The sample with added 5at.% TaB(2) and milled for 300 minutes showed values of J(c) similar to 7 x 10(5) A/cm(2) and F(p) similar to 14 GN/m(3) at 2T, 4.2 K. The milled and TaB(2)-mixed samples showed higher values of mu(0)H(irr) than the unmilled-unmixed sample.

Properties of Y-TZP/Al(2)O(3) ceramic nanocomposites obtained by high-energy ball milling

In this work, the synthesis of Y(2)O(3) stabilized tetragonal zirconia polycrystals (Y-TZP)-alumina (Al(2)O(3)) powder mixture was performed by high-energy ball milling and the sintering behavior of this composite was investigated. In order to understand the phase transformations occurring during ball milling, samples were collected after different milling times, from 1 to 60 h. The milled powders were compacted by cold uniaxial pressing and sintered at 1400 and 1600 degrees C. Both powders and sintered samples were characterized by X-ray diffraction (XRD), scanning electron microscopy (SEM), energy dispersive spectrometry analysis (EDS) and mechanical properties. Fully dense samples were obtained after sintering at 1600 degrees C, while the samples sintered at 1400 degrees C presented a full density for powder mixtures milled for 30 and 60 h. Fracture toughness and Vickers hardnessvalues of the Y-T-ZP/Al(2)O(3) nanocomposite were improved due to dispersed Al(2)O(3) grains and reduced ZrO(2) grain size. Samples sintered at 1400 degrees C, based on powders milled for 60 h, presented high K(IC) and hardness values near to 8.0 Mpan(1/2) and 15 GPa, respectively (C) 2008 Elsevier B.V. All rights reserved

Texture and mechanical properties evolution of a deep drawing medium carbon steel during cold rolling and subsequent recrystallization

Medium carbon steels are mostly used for simple applications; however, new applications have been developed for which good sheet metal formability is required. These types of steels have an inherent low formability. A medium-carbon hot-rolled SAE 1050 steel was selected for this study. It has been cold rolled with thickness reductions varying between 7 and 80%. The samples obtained were used to evaluate the strain hardening curve. For samples with a 50 and 80% thickness reduction, an annealing heat treatment was performed to achieve recrystallization. The material was characterized in the ""as-received"", cold rolled and annealed conditions using several methods: optical metallography, X-ray diffraction (texture), Vickers hardness, and tensile testing. For large thickness reductions, the SAE 1050 steel presented low elongation, less than 2%, and yield strength (YS) and tensile strength (TS) around 1400 MPa. Texture in the ""as-received"" condition showed strong components on the {001} plane, in the < 100 >, < 210 > and (110) directions. After cold rolling, the texture did not present any significant changes for small thickness reductions, however. It changed completely for large ones, where gamma, < 111 >//ND, alpha, < 110 > HRD, and gamma prime, < 223 >//ND, fibres were strengthened. After annealing, the microstructure of the SAE 1050 steel was characterized by recrystallized ferrite and globular cementite. There was little change in the alpha fibre for the 50% reduction, whereas for the 80% reduction, its intensity increased. Both gamma and gamma prime fibres vanished upon annealing for 50 and 80% reductions alike. (c) 2008 Elsevier B.V. All rights reserved.

Medium carbon steel deep drawing: A study on the evolution of mechanical properties, texture and simulations, from cold rolling to the end product

Medium carbon steels are mostly used for simple applications; nevertheless new applications have been developed for which good sheet formability is required. This class of steels has an inherent low formability. A medium carbon hot rolled SAE 1050 steel has been selected for this study. It has been cold rolled with reductions in the 7-80% range. Samples have been used to assess the cold work hardening curve. For samples with a 50 and 80% thickness reduction, an annealing heat treatment has been performed to obtain recrystallization. The material has been characterized in the ""as received"", cold rolled and annealed conditions, using several methods: optical microscopy, X-ray diffraction (texture), Vickers hardness and tensile testing. The 50% cold rolled and recrystallized material has been further studied in terms of sheet metal formability and texture evolution during the actual stamping of a steel toecap that has been used to validate the finite element simulations. (C) 2008 Elsevier B.V. All rights reserved.