Free Ball Research Articles

Planning the Initial Motion of a Free Sliding/Rolling Ball

This paper investigates the motion of a free ball with initial velocity and angular velocity on a horizontal plane under friction. The ball will first slide along a parabolic trajectory (with its contact velocity in constant direction) and then roll along a straight trajectory. Curving of the sliding trajectory can be utilized for obstacle avoidance in path planning. A one-to-one correspondence exists between curved trajectories of the ball from one point to another and pairs of sliding and rolling directions that span a cone at the starting point to contain the ending point in the interior. This leads to a compact 2-D trajectory space, in which obstacles induce monotonic constraint curves. Based on the monotonicity, a plane sweep algorithm is described to find all collision-free trajectories. The work has several distinct features: handling of both sliding and rolling; planning in the configuration space of trajectories not that of the ball; computation of not just one collision-free trajectory but all such trajectories; and, finally, combining dynamics with computational geometry. The application of the work to spherical robots is discussed at the end.

Decentralized adaptive sliding mode control of a space robot actuated by control moment gyroscopes

An adaptive sliding mode control (ASMC) law is proposed in decentralized scheme for trajectory tracking control of a new concept space robot. Each joint of the system is a free ball joint capable of rotating with three degrees of freedom (DOF). A cluster of control moment gyroscopes (CMGs) is mounted on each link and the base to actuate the system. The modified Rodrigues parameters (MRPs) are employed to describe the angular displacements, and the equations of motion are derived using Kane’s equations. The controller for each link or the base is designed separately in decentralized scheme. The unknown disturbances, inertia parameter uncertainties and nonlinear uncertainties are classified as a “lumped” matched uncertainty with unknown upper bound, and a continuous sliding mode control (SMC) law is proposed, in which the control gain is tuned by the improved adaptation laws for the upper bound on norm of the uncertainty. A general amplification function is designed and incorporated in the adaptation laws to reduce the control error without conspicuously increasing the magnitude of the control input. Uniformly ultimate boundedness of the closed loop system is proved by Lyapunov’s method. Simulation results based on a three-link system verify the effectiveness of the proposed controller.

Insectomorphic robot maneuvering on freely rolling balls

The influence of the position of the center of mass of a multilegged robot that moves along the surface of a freely rolling ball on the direction of rolling of this ball over a horizontal plane is studied. The case when the center of mass of this robot is shifted (in the plane that is perpendicular to the velocity vector) from the vertical axis that goes through the ball center is analyzed. Approximation formulas that allow one to estimate the radius of curvature of the trajectory of the center of a ball during turn are obtained under certain simplifying assumptions. It is found that a shift of the center of mass from the vertical axis that goes through the ball center inevitably produces a certain spin of the ball about this axis, complicating the task of maneuvering on this ball. The problem of insectomorphic robot maneuvering with two freely rolling balls on a horizontal plane is solved in the model formulation. The problem consists in moving a robot from a horizontal plane over to a movable ball, rolling this ball close to another free ball, and making the robot climb from the first ball to the second one and then back to the horizontal plane. The difficulty is that the mechanical system under consideration is highly unstable and is thus strongly influenced by execution errors. It is demonstrated constructively that the problem of the indicated interaction between a robot and two balls is fundamentally solvable, and a model robot is able to perform this task, although it is forced to shift its center of mass from the vertical axis in the process.

Self-balancing system of the disk on an elastic shaft

This paper presents an analysis of the automatic balancing of a rigid disk mounted on an elastic shaft. The balancing system consists of two drums at a variable distance from the disk and free balls (or rollers) inside the disk. The balls are able to change positions with respect to the rotor and compensate for rotor unbalance. This paper presents the equations of motion for the disk as well as for the balls during balancing. It is shown that the balls can compensate a part or all of the rotor unbalance depending on the positioning of the drums. There are vibratory forces that push the balls to new positions; these are responsible for the behavior of the balls and the final results. The vibratory forces are defined as a function of the system׳s parameters and they determine the position of equilibrium of the balls. The stability and efficiency of the method is analyzed in this paper.

Study of Micro-Abrasive Wear Resistance of Heat Treated NiTi Alloys

The Nickel Titanium (NiTi) alloy is a shape memory alloy. It presents two distinct properties: shape memory effect (martensite phase at room temperature) and the pseudoelasticity (austenite phase at room temperature). These materials are frequently used in industries like engineering, dentistry, medicine and aeronautics, and for certain applications it is important to know the wear behavior of these alloys.Thus, this study aims to evaluate the micro-abrasive wear behavior of pseudoelastic NiTi alloys at the as received and aged conditions, and compare with results obtained for NiTi alloy with shape memory effect. The aging heat treatment was performed at temperatures of 350, 450, 500 and 600 °C with an isotherm of 30 minutes and subsequent quenching in water. The wear tests were carried out in a free ball machine. After wear testing was observed that the wear coefficient obtained were lower for all treatment temperatures when compared to pseudoelastic NiTi alloy as received, reducing wear by 30 % in case of treatment at 350 °C. The alloy with shape memory effect showed good wear behavior, with a wear coefficient about 14 % less than the untreated pseudoelastic NiTi alloy.

Influence of deep cryogenic treatment of high speed steel substrate on TiAlN coating properties

AbstractDeep cryogenic treatment in combination with classic heat treatment shows a significant improvement in wear resistance of high speed steel tools. The aim of this research was to investigate how the microstructure of the substrate tool steel material, which was altered by deep cryogenic treatment and plasma nitriding, influences the properties of TiAlN coating. The microstructure, topography and composition of the TiAlN coating were investigated using field‐emission scanning electron microscope, atomic force microscopy, XRD, and glow discharge optical emission spectroscopy. The coating adhesion was measured using the scratch test. The sliding wear resistance and the force required to break the coating were determined with the ball‐on‐flat method. Resistance to microabrasion was measured by free ball abrasion test. The results show that deep cryogenic treatment combined with plasma nitriding influence the adhesion of the TiAlN coating to the high speed steel substrate. Wear resistance tests show better wear resistance of deep cryogenic treated samples in comparison with conventionally heat treated ones.

Wear behaviour of low carbon steel after severe shot peening

In this study, the shot peening process which is a mechanical surface treatment was applied to AISI 1017 low carbon steel material. The free ball micro abrasion test was applied to the specimens following the peening process. The applied shot peening conditions expose the specimens to higher plastic deformation than traditional shot peening and the aim was to establish fine grain structures on the surface and right underneath the surface. Conventional characterization techniques, such as optical microscopy, scanning electron microscopy and transmission electron microscopy were used to study the microstructure of the fine-grained layer. Microhardness measurements were also performed across the fine grained layer. As a result of the microstructure studies, it was observed that dislocation was extended as a result of plastic deformation in a layer of size 40 μm on the surface of the specimen. It was observed that the hardness and stiffness of the specimen surface increased due to the peening intensity, and the wear durability increased as a result.

골프 드라이버 임팩트 위치에 따른 소리 분석

This study was aimed to evaluate the characteristics of impact sound of golf driver according to impact points of its face. In order to get the consistent impact sounds, the apparatus for free golf ball drop was prepared and used. Timed amplitude patterns and maximum spectral peaks of the impact sounds were variant according to the impact points of driver face. As an alternative method of impact sound analysis, cumulative sum of spectral power (cumsum) was used to distinguish between impact sounds according to the impact positions. From the comparison of frequencies representing 20%, 40%, 60%, 80% of cumsum of impact sound, 40% cumsum frequency of the center of driver face was lower than that of the toe and the heel. This finding suggests that the impact sound from the center of driver face has higher spectral power of low frequency component than that of the toe and heel.

Influence of surface texturing and hard chromium coating on the wear of steels used in cold rolling mill rolls

The present work analyzed the wear behavior of surface modifications often used in cold rolling mill rolls. Different surface modifications were carried out on samples produced from a fragment of a rolling mill roll: i) shot blasting texturing using steel spheres (T); ii) chromium plating (C); iii) shot blasting texturing with subsequent hard chrome plating (TC); iv) and hard chrome plating with subsequent shot blasting texturing (CT). Before the surface modifications the samples were heat treated and ground on both faces. Sliding wear tests were performed using a reciprocating movement of a ball over flat configuration under a load of 9.8N. Abrasive wear tests used a free ball microabrasion tester with SiO2 abrasive particles. Surface texturing increased Sq, Sdq and Spk and reduced Sbi of the uncoated samples, i.e., the surface became rougher, whereas hard chrome coating after texturing did not alter much the surface topography, although a slight decrease of Spk and a slight increase of Sbi of the samples were detected i.e., a slight smoothening of the textured surfaces occurred due to chromium plating. The results of the reciprocating tests showed, after running in, average friction coefficients of 0.38±0.01 for all the samples tested, evidencing no significant change in the coefficient of friction as a function of surface modification. Surface texturing increased the sliding wear of the counterbodies when compared with that obtained by the sample without modification (WM) by 70% for 1h tests and by 35% for 10h tests. When the surface was textured before chromium plating, the wear rate of the counterbody did not increase in relation to the C sample for the 1h test, but was the highest for 10h tests, with an increase of 200% in relation to the C sample. On the other hand, chromium plating increased the wear rate of the specimens, for conditions either with or without previous texturing. The addition of the hard chromium coating promoted the formation of a tribolayer on the counterbody consisting of chromium and oxygen. For the samples without hard chrome coating, the tribolayer consisted of iron and oxygen and it was located on the specimen surface. The results of microabrasion showed that, for the uncoated samples, surface texturing increased abrasion resistance (24%). The reduction was higher (67%) for the coated samples, but previous texturing of the coated samples increased abrasion (54%) when compared with the coated samples.

Effect of laser surface modification on the micro-abrasive wear resistance of coated cemented carbide tools

The use of surface texturing on the rake face of a tool can modify the tribological phenomena present at the chip-tool interface. Many different wear mechanisms, including abrasive wear, occur at the tool during machining. The presence of hard phases in the workpiece material, as well as hard particles removed from the tool, can generate abrasive wear on the tool surfaces. The objective of this work is to study the abrasive wear resistance of micro-textured tools in comparison to conventional (commercial) cutting tools. Square cemented carbide inserts containing a three-layered coating (TiCN–Al2O3–TiN) were textured using two different linear patterns, perpendicular and parallel to the direction of the chip movement. Microabrasion and machining tests on both textured and commercial tools were carried out. Turning tests were carried out for ABNT/AISI 1050 steel under severe cutting conditions with overhead application of cutting fluid. In order to simulate the abrasive wear mechanism that can occur on the tool surface, a free ball microabrasion test was used under a suspension of silicon carbide particles and distilled water. The abrasive wear mechanisms were observed using SEM. The micro-scale abrasive wear resistance of laser micro-textured cement carbide tools was compared to untextured tools. For the turning tests, texturing increased the tool life, which was determined when the wear at the tool flank achieved a specified value. On the other hand, for the microabrasion tests, laser texturing resulted in a pronounced increase in the coating wear rate. This fact was connected to the decrease of coating hardness caused by laser texturing. Therefore, the increase of tool life in the turning tests was not related to a reduction of abrasive wear on the tool flank. Probably, it was caused by other tribological conditions that were not represented in microabrasion tests, for example: the presence of cutting fluid in the environment and elevated contact temperatures.

Stainless steel as an antiwear material for the bio-fuel industry

In the 1980s, Brazil started a national program to use bio-fuels as one its main energy sources, in particular ethanol produced from sugar cane. Since then, the increase of production and efficiency in the crop fields has drastically reduced the period available for the annual maintenance of the industrial plants. One of the main reasons for the annual maintenance is premature wear of devices used to wash, cut and crush sugar cane. Samples of components of such devices were collected from different sugar plants and had their wear mechanisms characterized by SEM and laser interferometry. The predominant wear mechanisms were sliding and rolling of abrasive particles and corrosion. In order to reproduce these wear mechanisms, both a lapping-like tester using large soft abrasive particles and a free ball micro-abrasion tester using fine soft abrasive particles were used. A structural carbon steel (reference material) was compared with a low alloy steel and different stainless steels, using dry and wet versions of each tester. For tests where the rolling of abrasive particles predominated, all stainless steels presented superior performance, especially under wet conditions. On the other hand, for tests with predominance of particle sliding, the low alloy steel was superior under dry conditions, but under wet conditions, with a corrosive component, stainless steels performed better. The pilot use of these laboratorial results in three industrial plants, where abrasive and corrosive conditions coexist, showed their excellent correlation with field tests. The use of stainless steel increased wear life, corroborating the importance of the synergistic effect between corrosion and abrasion. With the successful results obtained with the pilot substitution of some parts that were conventionally manufactured using carbon steel by similar parts in stainless steel, which started in 2003, this substitution increased, so that since 2007 almost all parts in the initial stages of sugar cane processing in the main Brazilian industrial plants have been manufactured using P410D stainless steel.

How to control the Chaplygin ball using rotors. II

In our earlier paper [3] we examined the problem of control of a balanced dynamically nonsymmetric sphere with rotors with no-slip condition at the point of contact. In this paper we investigate the controllability of a ball in the presence of friction. We also study the problem of the existence and stability of singular dissipation-free periodic solutions for a free ball in the presence of friction forces. The issues of constructive realization of the proposed algorithms are discussed.

Failure mode in sliding wear of PEEK based composites

Polymers and polymer composites are commonly used as solid lubricants. Polyether–ether–ketone (PEEK) is an engineering thermoplastic with a very good combination of thermal and mechanical properties. Although PEEK presents relatively high friction coefficients during unlubricated sliding, the wear rates are remarkably low. Despite this potential as a good tribological material, the high performance abilities of PEEK have not been entirely realized in practice because PEEK-ferrous metal contacts may fail by scuffing and/or two-three body abrasion for certain tribosystems. The traditional design approach to reinforce PEEK has been to use fibres for strengthening and filler particles for lubrication. In this work three materials were analysed: PEEK, carbon-fibre (CF) reinforced PEEK and PTFE+Graphite+CF filled PEEK. A series of different tribo-tests was carried out: (i) Reciprocating linear scuffing test with 7N incremental loading every 10min up to 910N; (ii) constant load (10N, 5h duration), reciprocating sliding tests assessing friction coefficient and wear rates of both specimen and counter body; (iii) free ball micro-abrasion tests using soft, fine abrasive particles. The wear tracks were analysed using SEM and light interferometry in order to assess the morphology of the wear tracks during scuffing, abrasion and sliding tests. The aim was to identify whether the failure mode in the sliding wear of these PEEK based materials is dominated by scuffing or by abrasive mechanisms. Unfilled PEEK exhibited very low scuffing resistance and a large wear rate during reciprocating sliding wear and abrasion, presenting a clear tendency to fail by abrasion mechanisms. CF-reinforced PEEK also presented very low scuffing resistance but higher sliding and micro abrasive wear resistance. It seemed that the presence of CF enhanced protection against abrasion by minimizing plastic deformation, although flaky debris probably originated from subsurface cracking were observed. The addition of PTFE and Graphite to the CF-reinforced PEEK produced a sharp decrease in friction coefficient, high scuffing and abrasion resistance, with an almost non-measurable wear rate in the reciprocating sliding test. The behaviour observed for PTFE+Graphite+CF filled PEEK suggested the transfer of a protective tribo-layer from the composite to the counter-body and vice-versa.

Effects of Corner/Edge Bonding and Underfill Properties on the Thermal Cycling Performance of Lead Free Ball Grid Array Assemblies

Underfilling will almost certainly improve the performance of an area array assembly in drop, vibration, etc. However, depending on the selection of materials, the thermal fatigue life may easily end up worse than without an underfill. This is even more true for lead free than for eutectic SnPb soldered assemblies. If reworkability is required, the bonding of the corners or a larger part of the component edges to the printed circuit board (PCB), without making contact with the solder joints, may offer a more attractive materials selection. A 30 mm flip chip ball grid array (FCBGA) component with SAC305 solder balls was attached to a PCB and tested in thermal cycling with underfills and corner/edge bonding reinforcements. Two corner bond materials and six reworkable and nonreworkable underfills with a variety of mechanical properties were considered. All of the present underfills reduced the thermal cycling performance, while edge bonding improved it by up to 50%. One set of the FCBGAs was assembled with a SnPb paste and underfilled with a soft reworkable underfill. Surprisingly, this improved the thermal cycling performance slightly beyond that of the nonunderfilled assemblies, providing up to three times better life than for those assembled with a SAC305 paste.

Effect of nature of nitride phases on microabrasion of plasma nitrided sintered iron

In the present investigation, the effect of plasma nitriding on the microabrasion behaviour of sintered unalloyed iron is investigated. Plasma nitriding was carried using two different sets of operative parameters in order to produce microstructures composed of different dominants iron nitrides, e.g.Fe4N (y´) and Fe2–3N(e), phases. Microabrasive wear tests were carried out in a 'free ball' microabrasion tester using SiC slurries. The tribological parameters were kept constant during the tests. The microstructures constituted of e-(Fe2–3N) phase presented a superior abrasion resistance.

Abrasive wear mechanisms of multi-components ferrous alloys abraded by soft, fine abrasive particles

In this paper, the effect of micro structural parameters (eutectic carbides and matrix hardness) on the micro abrasive wear of multi- component ferrous alloys abraded by soft, fine abrasive particles is analysed. Two series of quenched and tempered alloys with variable vanadium or molybdenum contents and fixed amounts of other elements were tested. Each series includes an alloy free of carbides (matrix alloy) and alloys containing carbides (carbide rich alloys). Heat treatment produced three different levels of matrix hardness. Free ball micro-abrasion tests were conducted using SiO2 fine abrasives. The results showed that the wear coefficient was not influenced by either the nature and amount of eutectic carbides or by the hardness of the matrix. Matrix alloys showed a considerably higher micro abrasive wear rate (up to 5 times) than eutectic carbide rich alloys. Special emphasis was given to the wear mechanisms, characterized by Scanning Electron Microscopy and Laser interferometry. Analysis of transversal sections produced by Focused Ion Beam and High Resolution Scanning Electron Microscopy showed that the removal of matrix material due to abrasion with fine silica particles decreased the mechanical support for the carbides, which caused gradual fracture and their pull-out.

A 1200V High-Power Driver IC with Multi-Chip Mounting for Strong HEVs

1200V high-power IC for Hybrid Electric Vehicles (HEVs) was developed for the first time. This IC consists of the 30V lower and upper arm ICs fabricated by Silicon On Insulator (SOI) process, 1200V discrete power MOSFETs for level shift circuit, and 30V discrete power MOSFETs for the output stage. The chips were mounted by BGA (Ball Grid Array) technology with Pb free solder balls. With these technologies, the high blocking voltage of 1200V was achieved without a special high-voltage IC process. In addition, the soft and low loss switching was realized by combination of high power output stage and the soft gate circuits, which this power IC can drive an Insulated Gate Bipolar Transistor (IGBT) even for over 100kW class inverter.

Validated High Speed Pull and Shear Test Methodologies to Evaluate Pb-Free BGA Mechanical Strength

The conversion to lead free Ball Grid Array (BGA) packages has raised several new assembly and reliability issues. Lead-free solder joints are generally stiffer than tin-lead solder joints, and mechanically induced failures have become more prevalent in lead-free solder assemblies. Traditionally, assembly bend and shock testing is performed to evaluate mechanical assembly reliability. However, bend and shock tests are expensive, cumbersome and not feasible for evaluating lot-to-lot variations in mechanical strength. Consequently, there is a need for a validated, component level test method that can be used as an accurate indicator of assembly level mechanical strength. Several publications have been written to evaluate the efficacy of high speed pull and shear testing as a viable reliability indicator [1 – 10]. In this study, a comprehensive Gauge R&R study was performed to evaluate the accuracy of the test equipment, including high speed video calibration. Then, test studies were performed to compare the accuracy of the results, spread across different package constructions, solder metallurgies, ball pitch and surface finish. In addition, the effect of parameters like multiple reflows and aging on specific metallurgies and surface finishes was studied. The results were generated over more than 2000 test runs. Finally, the study rank orders all critical test parameters and articulates what precise steps can be taken to generate relevant data for standard and custom devices during early evaluation stages and during high volume manufacturing.

On the validation of DEM and FEM/DEM models in 2D and 3D

PurposeAs particulate systems evolve, sliding, rolling and collision contacts all produce forces that discrete element method (DEM) methods aim to predict. Verification of friction rarely takes high priority in validation studies even though friction plays a very important role in applications and in mathematical models for numerical simulation. The purpose of this paper is to address sliding friction in finite element method (FEM)/DEM and rolling friction in DEM.Design/methodology/approachAnalytical solutions for “block sliding” were used to verify the authors' tangential contact force implementation of 2D FEM/DEM. Inspired by the kinetic art work Liquid Reflections by Liliane Lijn, which consists of free balls responding within a rotating shallow dish, DEM was used to simulate rolling, sliding and state‐of‐rest of spherical particles relative to horizontal and inclined, concave and flat spinning platforms. Various material properties, initial and boundary conditions are set which produce different trajectory regimes.FindingsSimulation output is found to be in excellent agreement when compared with experimental results and analytical solutions.Originality/valueThe more widespread use of analytically solvable benchmark tests for DEM and FEM/DEM codes is recommended.

Tribological characteristics of WC-based claddings using a ball-cratering method

Abstract Tungsten carbide-based thick coatings are used as wear resistant claddings or surface overlays in industrial applications to counter erosive and/or abrasive wear problems. Three-body abrasive wear behaviour of infiltration brazed tungsten carbide (WC) claddings was investigated using a ball-cratering method, a version with a free ball, with slurry containing 150–300 μm silica sand particles. Three WC claddings tested had different volume fractions and size distribution of carbides that resulted in their different bulk hardness and the matrix was a Ni–Cr based alloy. It was found that the wear rates of all WC claddings were almost constant with testing time or distance travelled by a rotating ball. The wear rates were independent of the slurry delivery rate and did not increase with increasing rotating ball roughness. The wear rates were affected by the material characteristics of WC claddings such as the volume fraction of carbides, directly related to bulk hardness, and carbide size distribution. SEM examination found that three-body rolling wear was a dominating wear mechanism. The softer matrix was worn out preferentially, leaving behind protruding and weakly-supported carbides. Small solid carbides were then dislodged and larger cemented WC/Co carbides were gradually worn out by a combination of microcracking and attrition. The abrasive characteristics of WC claddings in the ball-cratering tests were then compared to the characteristics of nominally identical materials in the standard ASTM G65 and G76 tests, as reported in the literature, and similarities and differences found are reported. Also, the in-field wear mechanisms found in the WC cladding were compared to the mechanisms observed in the ball-cratering tests.