Academic literature on the topic 'Falling ball dynamics'

Cageless ball bearings are often preferred as a back-up bearing for active magnetic bearings to support a falling rotor, but the contact between the balls of the cageless ball bearing may lead to the deterioration of the bearing performance and affect the dynamic stability of the rotor system. Thus, we studied the discrete dynamics of cageless ball bearings. First, a model is proposed to change the groove curvature center of the local outer raceway to control the ball velocity to achieve dispersion. Combined with the spatial geometry theory, the mathematical model of the discrete raceway is established, the collision between the balls is considered as an abruptly added constraint, and the non-smooth dynamics equation of the cageless ball bearing with a local discrete raceway is established. Then, the fourth-order Adams prediction correction algorithm is used to numerically solve the dynamic discretization of the ball, and the structural parameters of the discrete raceway are preferably selected, according to the phase diagram of the ball and the change in the angular spacing. The results show that the structure of the discrete raceway has a strong influence on the discrete dynamics of the ball.

In fluid dynamics and related fields, accurately measuring liquid viscosity is vital. The traditional falling ball method, common in education and research, faces challenges in ensuring uniform fall and correcting for phenomena like eddy currents. This thesis introduces a new device based on the Poiseuille method, measuring viscosity through pressure difference and adjustable flow rates. Comparing it with the falling ball method, we found the latter has an average error of 5.21%, while the Poiseuille method has only 1.23%. The Poiseuille method avoids issues like Reynolds coefficient correction and inaccuracies from high ball speeds, offering stability and practical value.

Dropping a water-filled cup with a ping-pong ball inside to the ground expels the ball much higher than its initial height. During free fall, the absence of gravity in the reference frame of the cup makes capillary forces dominant, causing the ball to be sucked into water. At impact, the high velocity ejection is due to the strong Archimedes’ force caused by vertical acceleration. In this paper, we study the dynamics of the capillary sinking of the ball during free fall and the ejection speed at impact, using tracking and high-speed imaging. In particular, we show that at short-time, the sinking is governed by capillary and added mass forces.

AbstractThe dynamics of flowing, concentrated suspensions of non-colloidal particles continues to surprise, despite decades of work and the widespread importance of suspension transport properties to industrial processes and natural phenomena. Blanc, Lemaire & Peters (J. Fluid Mech., 2014, vol. 746, R4) report a striking example. They probed the time-dependent dynamics of concentrated suspensions of rigid and neutrally buoyant spheres by simultaneously measuring the oscillatory rheology and the sedimentation rate of a falling ball. The sedimentation velocity of the ball through the suspension depends strongly on the frequency of oscillation, though the rheology was found to be independent of frequency. The results demonstrate the complexities of suspension flows and highlight opportunities for improving models by exploring suspension dynamics and rheology over a wide range of conditions, beyond steady and unidirectional ones.

Humans demonstrate an amazing ability for intercepting and catching moving targets, most noticeably in fast-speed ball games. However, the few studies exploring the neural bases of interception in humans and the classical studies on visual motion processing and visuomotor interactions have reported rather long latencies of cortical activations that cannot explain the performances observed in most natural interceptive actions. The aim of our experiment was twofold: (1) describe the spatio-temporal unfolding of cortical activations involved in catching a moving target and (2) provide evidence that fast cortical responses can be elicited by a visuomotor task with high temporal constraints and decide if these responses are task or stimulus dependent. Neuromagnetic brain activity was recorded with whole-head coverage while subjects were asked to catch a free-falling ball or simply pay attention to the ball trajectory. A fast, likely stimulus-dependent, propagation of neural activity was observed along the dorsal visual pathway in both tasks. Evaluation of latencies of activations in the main cortical regions involved in the tasks revealed that this entire network of regions was activated within 40 msec. Moreover, comparison of experimental conditions revealed similar patterns of activation except in contralateral sensorimotor regions where common and catch-specific activations were differentiated.

Prevailing views on how we time the interception of a moving object assume that the visual inputs are informationally sufficient to estimate the time-to-contact from the object's kinematics. Here we present evidence in favor of a different view: the brain makes the best estimate about target motion based on measured kinematics and an a priori guess about the causes of motion. According to this theory, a predictive model is used to extrapolate time-to-contact from expected dynamics (kinetics). We projected a virtual target moving vertically downward on a wide screen with different randomized laws of motion. In the first series of experiments, subjects were asked to intercept this target by punching a real ball that fell hidden behind the screen and arrived in synchrony with the visual target. Subjects systematically timed their motor responses consistent with the assumption of gravity effects on an object's mass, even when the visual target did not accelerate. With training, the gravity model was not switched off but adapted to nonaccelerating targets by shifting the time of motor activation. In the second series of experiments, there was no real ball falling behind the screen. Instead the subjects were required to intercept the visual target by clicking a mousebutton. In this case, subjects timed their responses consistent with the assumption of uniform motion in the absence of forces, even when the target actually accelerated. Overall, the results are in accord with the theory that motor responses evoked by visual kinematics are modulated by a prior of the target dynamics. The prior appears surprisingly resistant to modifications based on performance errors.

There are needed energy (heat) accumulators to increase the efficiency of solar installations, including solar collectors (water heaters, air heaters, dryers). One of the tasks of designing heat accumulators is to ensure its minimal heat loss. The article considers the problem of determining the distribution of temperatures and heat losses by convection and radiation of the heat insulation-accumulating body (water) system for a ball heat accumulator under symmetric boundary conditions. The problem is solved numerically according to the program developed on the basis of the proposed «gap method». (Research purpose) The research purpose is in determining heat losses by convection and radiation of a two-layer ball heat accumulator with symmetric boundary conditions. (Materials and methods) Authors used the Fourier heat equation for spherical bodies. The article presents the determined boundary and initial conditions for bodies and their surfaces. (Results and discussion) The thickness of the insulation and the volume of the heat accumulator affect the dynamics and values of heat loss. The effect of increasing the thickness of the thermal insulation decreases with increasing its thickness, starting with a certain volume of the heat accumulator or with R > 0.3 meters, the heat losses change almost linearly over time. The dynamics of heat loss decreases with increasing shelf life, but the losses remain large. (Conclusions) Authors have developed a method and program for numerical calculation of heat loss and temperature over time in a spherical two-layer heat accumulator with symmetric boundary conditions, taking into account both falling and intrinsic radiation. The proposed method allows to unify the boundary conditions between contacting bodies.

The steady-state shear viscosity of low-concentrated Poly(2-ethyl-2-oxazoline) (PEOX) aqueous solutions is measured near the presumed theta temperature using the falling ball viscometry technique. The experimental data are analyzed within the model that joins the Rouse and Zimm bead-spring theories of the polymer dynamics at the theta condition, which means that the polymer coils are considered to be partially permeable to the solvent. The polymer characteristics thus depend on the draining parameterhthat is related to the strength of the hydrodynamic interaction between the polymer segments. The Huggins coefficient was found to be 0.418 at the temperature 20°C, as predicted by the theory. This value corresponds toh= 2.92, contrary to the usual assumption of the infiniteh. This result indicates that the theta temperature for the PEOX water solutions is 20°C rather than 25°C in the previous studies. The experimental intrinsic viscosity is well described coming from the Arrhenius equation for the shear viscosity.

In this study, dynamic hardness tests on solid and engineered wood flooring specimens of Eucalyptus globulus Labill. and Eucalyptus grandis W. Hill ex Maiden hardwoods were performed because nowadays, these fast-growing hardwoods are still scarcely employed for this use. Furthermore, another two examples of hardwood commonly applied on wood flooring, Quercus robur L. and Hymenaea courbaril L., were also tested. To compare their properties, a dynamic impact hardness test based on the impact of steel balls, with several diameters, and drop heights was developed. Accordingly, 120 solid wood flooring specimens and 120 engineering wood flooring specimens were producing with these four hardwood species. Dynamic impact tests were made with three steel balls of different diameters (30–40–50 mm), and they were carried out from five different drop heights (0.60–0.75–0.90–1.05–1.20 m). The impact of the steel ball drew the size of the footprint on the surface and this mark was measured with a digital caliper for both dimensions, diameter and depth, as footprint diameter (FD) and indentation depth (ID). Data from 3000 samples, corresponding to 120 different individual groups (4 species × 3 ball diameters × 5 drop height × 2 floor type) were analyzed. Results indicated that the variability of ID (CV between 19.25–25.61%) is much greater than the values achieved for FD (CV between 6.72–7.91%). Regarding the fast-growing hardwood species tested, E. globulus showed a similar behavior to traditional hardwood applied on wood flooring in Europe, Q. robur, and it could be a promising growth in the flooring industry. However, E. grandis showed the worst values compared to traditional hardwood in all test configurations.

Abstract: Viscosity is the one of the major parameters to be considered in fluid related experiments and also in many industries. A new method of calculation of Dynamic Viscosity using the Viscometer which is easy for experimentation, with less calculation efforts, simple in design, construction with min. investment and no or minimum maintenance. This Paper intends to find the viscosity of Opaque fluids using falling ball viscometer. Falling Ball Viscometer works with Strokes law as the correction factor is multiplied in the calculation. As the correction factor is derived from the outcomes from the experiment and C-Code was written to make the calculation more efficient.

Cette thèse présente une investigation approfondie, mettant en œuvre des approches expérimentales et numériques, sur un viscosimètre à chute de bille modifié utilisé pour déterminer les propriétés rhéologiques des fluides. Le fluide étudié ici est le Carbopol, modélisé comme un fluide de type Herschel-Bulkley. Il s'agit d'une gamme de fluides appelés fluides viscosplastiques, caractérisés par une contrainte seuil d'écoulement et d'un comportement rhéofluidifiant sous écoulement. Initialement, la configuration classique du viscosimètre, à savoir une bille soumise à la gravité tombant dans un tube rempli de fluide viscoplastique, a été analysée expérimentalement. Les résultats expérimentaux pour cette configuration classique concordent avec la littérature : pour de faibles valeurs de contrainte seuil, la bille tombe avec une vitesse verticale constante. L'analyse des données obtenues dans ces conditions a révélé des effets de confinement, mettant en évidence le défi de la reproductibilité dans l'expérience classique de la boule tombante. Pour résoudre cette problématique, une nouvelle configuration de viscosimètre a été proposée en introduisant un aimant permanent dans le système pour contrôler la dynamique de la bille lors de sa chute, assurant ainsi des données reproductibles. Dans ce nouvel dispositif, la compréhension de toutes les forces agissant sur la bille et leur influence sur sa dynamique est cruciale. Tout d'abord, les efforts se sont portés sur la détermination de la force magnétique par des approches analytiques et numériques, validées par des mesures expérimentales. Les trajectoires des données expérimentales du viscosimètre modifié ont ensuite été comparées pour valider le calcul de cette force nouvellement ajoutée. Les résultats démontrent que tandis que l'analyse de la position radiale reste difficile, les données de position verticale concordent avec les simulations. Afin de compléter les données de la littérature, la force de traînée seule a également été étudiée dans la configuration classique du viscosimètre. Un développement détaillé a été réalisé pour étudier la force de traînée statique, le résultat obtenu correspond la valeur bien connue de la littérature. Par des approches analytiques et numériques, nous aboutissons à une nouvelle corrélation pour le coefficient de traînée qui inclue cette force statique, les propriétés rhéologiques du fluide d'Herschel-Bulkley mais aussi les paramètres géométriques, notamment le rapport des rayons du tube et de la bille. Ce travail enrichit la littérature existante en fournissant de résultats originaux et en présentant de nouvelles perspectives par l'ajout d'une force de volume connue qui vient modifier la dynamique de la bille
This thesis presents an in-depth investigation, using experimental and numerical approaches, on a modified falling ball viscometer used to determine the rheological properties of fluids. The fluid studied here is Carbopol, modeled as a Herschel-Bulkley type fluid. This is a range of fluids called viscoplastic fluids, characterized by a yield stress and shear-thinning behavior under flow. Initially, the classic configuration of the viscometer, i.e., a ball subject to gravity falling in a tube filled with viscoplastic fluid, was analyzed experimentally. The experimental results for this classic configuration align with the literature: for low yield stress values, the ball falls with a constant vertical velocity. The analysis of the data obtained under these conditions revealed confinement effects, highlighting the challenge of reproducibility in the classic falling ball experiment. To address this issue, a new viscometer configuration was proposed by introducing a permanent magnet into the system to control the dynamics of the ball during its fall, thus ensuring reproducible data. In this new device, understanding all the forces acting on the ball and their influence on its dynamics is crucial. First, efforts focused on determining the magnetic force through analytical and numerical approaches, validated by experimental measurements. The trajectories of the experimental data from the modified viscometer were then compared to validate the calculation of this newly added force. The results show that while the analysis of the radial position remains difficult, the vertical position data align with the simulations. To complement the literature data, the drag force alone was also studied in the classic viscometer configuration. A detailed development was carried out to study the static drag force, and the result obtained matches the well-known value in the literature. Through analytical and numerical approaches, we arrive at a new correlation for the drag coefficient that includes this static force, the rheological properties of the Herschel-Bulkley fluid, as well as geometric parameters, notably the tube-to-ball radius ratio. This work enriches the existing literature by providing original results and presenting new perspectives by adding a known volumetric force that modifies the ball’s dynamics

This scientific study considers the results of a computer experiment with heterogeneous elements (spheres) that proved to be of decisive importance during the separation process, namely their degree of activity, mobility and falling. It has been found that a detailed analysis of the Liapunov function indices allows to effectively understand and predict the dynamics of complex dynamical systems. The results obtained indicate significant changes in the physical and mechanical parameters of spherical balls under the influence of various factors and the environment. It was found that a certain accumulation of spheres occurs due to an increase in the time for simulation. It was also found that the key characteristics of the bulk mass of spherical elements significantly depend on the moulding process, surface condition and environmental conditions.

Hydraulic fluid is one of the most important components in every fluid power system. Therefore, fluid properties have to be known with a good accuracy in an increasing number of applications, for example in system’s design, modelling and control. The fluid of interest may be a power transmission fluid as well as a fuel. In defining the needed fluid characteristics, the large variety of different fluid types sets many demands for a single measuring system. Moreover, known fluid properties, of fuels in particular, are needed at constantly higher pressures and temperatures, raising the bar for practical measuring concepts — user-friendliness, safety and equipment cost are also essential criteria. In this paper, two accurate, but rather simple and affordable measuring concepts are presented. The speed of sound in a fluid, hydraulic fluid density and adiabatic tangent fluid bulk modulus are all defined with a direct measurement of the pressure wave propagation. The dynamic and kinematic fluid viscosities are defined with a remotely operated, modified falling ball viscometer. Both the presented methods have been developed further from the previously published concepts of the same authors. With these improved systems, all the mentioned fluid parameters can reliably be measured at up to at least 2,500 bar and at up to at least +150°C. Moreover, the same equipment can be applied to any type of hydraulic fluid, a fuel or a power transmission fluid, regardless of the base fluid, additives or viscosity grade. In addition to presenting the measuring concepts and the equipment used in detail, a selected sample of experimental results will also be presented to demonstrate the performance characteristics of the methods.

Abstract Innovative methods to enhance oil recovery efficiency remain a high priority in the energy sector. This study investigates the potential of magnesium oxide (MgO) nanoparticles, both alone and with sodium dodecyl sulfate (SDS) surfactant, to improve oil recovery by reducing the interfacial tension (IFT) between oil and water. The research focuses on the physicochemical properties of MgO nanoparticles and their efficacy in IFT reduction, critical for Enhanced Oil Recovery (EOR). Preparation of MgO nanofluids was achieved using a Magnetic Stirrer and Sonics Vibracell VCX 750 Ultrasonic Homogenizer to ensure thorough mixing and dispersion. Characterization involved measuring density with Calibrated Density Bottles, dynamic and kinematic viscosity using a Falling Ball Viscometer, pH levels with an Electronic pH meter, and electric potential difference (mV). The Malvern Zetasizer Nano ZS assessed Zeta Potential (mV), Electric Conductivity (mS/cm), and Electrophoretic mobility (µmcm/Vs) for both the nanofluid and the surfactant-nanofluid systems. Paraffin oil served as the oil phase, with nanoparticle (NP) concentrations tested at 0.01, 0.03, 0.05, 0.1, and 0.5 wt%. The SDS concentration remained constant at 0.5 wt% throughout the study. We employed Pendant Drop Interfacial Tension measurements to evaluate the oil-water, oil-nanofluid, and oil-nanofluid + surfactant systems. Significant IFT reduction was observed—from 47.9 to 26.9 mN/m with a 0.1 wt% MgO nanofluid. Even a minimal concentration of 0.01 wt% MgO NP decreased notably from 47.9 to 41.8 mN/m. An IFT reduction of up to 70% was noted when MgO NPs were combined with SDS. This IFT reduction enhances oil mobility, suggesting the MgO-SDS system as an effective EOR technique. The study also recorded shifts in Zeta Potential from −2.54 to 3.45 mV and more alkaline pH levels from 8.4 to 10.8, indicating the nanofluid's altered surface charge and interaction dynamics. These physicochemical changes, aided by SDS, improved the dispersion and stability of MgO nanoparticles at the oil-water interface, thus boosting oil displacement efficiency. These findings highlight the potential of the MgO-SDS system as a cleaner alternative to traditional EOR methods that use toxic chemicals, offering economic benefits from enhanced reservoir performance. However, practical challenges remain, including ensuring nanoparticle stability and compatibility under diverse reservoir conditions, managing surfactant adsorption, and scaling up to field-level operations. Future research must address these issues while maintaining interdisciplinary collaboration and rigorous field studies. In conclusion, incorporating MgO nanoparticles and SDS surfactant presents a promising approach to improving oil recovery efficiency. Further investigation into its field application and economic feasibility is essential to gauge the potential of this technology in the energy industry.

Abstract Bubble soccer is a recreational soccer game that has gained huge popularity in recent years. In this modified soccer game, the players are strapped inside the hollow region of a “donut” shaped inflatable membrane, in a fashion similar to how a backpack is worn. Due to the large sizes of bubble membrane, collision among players is a major component of bubble soccer games, which often results in the players falling over and hitting the ground at high impact speed. To ensure that the player’s head doesn’t come in contact with the ground, Bubble ball Business Association (BBA) [3] recommends a minimum clearance of 20.3 cm between the player’s head and the top surface of the bubble membrane. This criteria, however, depends on the structural rigidity of the bubble ball, which is a function of its inflation pressure. This paper presents the results from a series of Finite Element studies, which sought to investigate the dynamic behavior of both bubble ball and soccer players in the aftermath of a vertical impact (with the player’s head and bubble ball both being upside-down), at gauge inflation pressures ranging from 3.45 kPa to 17.25 kPa, with the BBA specified head clearance. Even though vertical impacts of such nature are extremely unlikely in bubble soccer, it was preferred over oblique ground impacts as vertical impacts is capable of causing more sever impacts. Additionally, the results from the vertical studies can also serve as recommendations for side impacts with vertical walls and for head-on collisions among players. In all simulations, a medium sized bubble ball was considered with a player mass of 100 kg (25% more than BBA specification). The results showed that the player’s head, at a minimum inflation pressure of 10.35 kPa, would preserve 88% of the initial 20.3 cm clearance value, in the aftermath of impact. At pressures lower than this minimum value, it was observed that the ball didn’t inflate enough, and thus, wasn’t structurally rigid, to exert sufficient lateral force on the player’s body. As a consequence, the frictional force at the player-ball interface in the direction opposite to the impact was also low, which resulted in the player’s head hitting the ground. Since 10.35 kPa is a relatively high inflation pressure, it can cause significant damage of the internal organs of the player during impact, as well as can cause discomfort during the game. This may trigger the players to reduce the inflation pressure, which as these studies show, has dangerous consequences. Thus, further studies were conducted by increasing the initial clearance of the head to the ball’s top surface from 20.3 cm to 25.4 cm and 30.5 cm, which showed that the ball would prevent the head from hitting the ground at inflation pressures of 6.9 kPa and 1.725 kPa respectively. Thus, if the position of the strap within the ball is adjusted allowing for higher head clearance, lower inflation pressures are sufficient to prevent head injuries, which will improve the overall safety associated with bubble soccer. To improve current studies, more sophisticated human body models must be integrated in the simulations, which will allow the analysis of damages to the internal organs. Additionally, physical experiment must be conducted to validate current computational results.