Ball Elements Research Articles

Dynamic behaviour of new anchor cable ribbed rockfall retaining walls on rock shed

This study investigates the dynamic behaviour between a rockfall and a new anchor cable ribbed rockfall retaining wall on a rock shed, by way of numerical simulations involving the coupling between the PFC3D (discrete-element method (DEM)) and Flac3D (finite-difference method (FDM)) software programs. The novel structure is modelled by the FDM through the zone element, while the rockfall and the buffer layer are modelled by the DEM through the ball element. The numerical results show that three stages of the rockfall movement were modelled: movement, impact and stagnation. The rockfall falls on the slope, impacting the buffer layer on the top of the rock shed, before rebounding to the anchored rockfall retaining walls (with a height lower than 2 m). Then, the stress and deflection can be unified and related to the impact velocity of the rockfall to examine the stability of the structure. The rockfall radius is the dominant of the three parameters (rockfall shape, rockfall radius and impact velocity). While the study focuses on a specific case study, the results provide valuable guidelines for future applications of the proposed combined structure for railway transportation protection.

Study on the vibration characteristics of deep groove ball bearings under time-varying loads

A general methodology for dynamic modeling and analysis of deep groove ball bearing used in the crank-slider mechanism of punching machine is presented in this paper. The time-varying loads applied at the inner ring of this bearing can be obtained by analyzing the planar multibody systems. The bearing joint has been modeled by introducing a nonlinear constraint force system, which takes into account the contact stiffness interaction between the rolling elements and the raceways. The four-degree-of-freedom dynamic equations for the inner and outer rings of the bearings is established by Newton's second law. By numerical calculation, the variations of the load, trajectory, FFT frequency domain response, and x direction phase trajectory and Poincare of the inner ring, and the contact force on each ball element are discussed. The results indicate that the present methodology can not only be used to analyze the overall dynamic behavior of crank-slider mechanism and the deep groove ball bearing used in punching machine, but also to obtain the dynamic loads of the inner ring and ball in bearing. Therefore, the dynamic loads on ball elements can provide a basis for the strength checking, fatigue life calculation and wear analysis of the deep groove ball bearing.

New Properties and Sets Derived from the 2-Ball Fractal Dust

Due to their practicality and convenient parametrization, fractals derived from iterated function systems (IFSs) constitute powerful tools widely used to model natural and synthetic shapes. An IFS can generate sets other than fractals, extending its application field. Some of such sets arise from IFS fractals by adding minimal modifications to their defining rule. In this work, we propose two modifications to a fractal recently introduced by the authors: the so-called 2-ball fractal dust, which consists of a set of balls diminishing in size along an iterative process and delimited by an enclosing square. The proposed modifications are (a) adding a resizer parameter to introduce an interaction between the generator and generated ball elements and (b) a new fractal embedded into the 2-ball fractal dust, having the characteristic of filling zones not covered by the previous one. We study some numerical properties of both modified resulting sets to gain insights into their general properties. The resulting sets are geometrical forms with potential applications. Notably, the first modification generates an algorithm capable of producing geometric structures similar to those in mandalas and succulent plants; the second modification produces shapes similar to those found in nature, such as bubbles, sponges, and soil. Then, although a direct application of our findings is beyond the scope of this research, we discuss some clues of possible uses and extensions among which we can remark two connections: the first one between the parametrization we propose and the mandala patterns, and the second one between the embedded fractal and the grain size distribution of rocks, which is useful in percolation modeling.

Characteristics of a safety-overrunning ball-type clutch in overload mode

Problem. The article investigates the operation of a ball safety-overrunning clutch in the overload mode. It is shown that its operation occurs in two stages – the initial one, when the balls retain engagement with the grooves, and the final one, when the balls are disengaged from the grooves of the outer half-clutch. Methodology. By analyzing the geometry of the clutch, expressions for calculating the geometric and kinematic relationships between the parts of the clutch at both stages of its operation were obtained. Results. The obtained results also make it possible to perform technological calculations necessary for the manufacture of clutch parts with helical grooves – the length of the mill stroke and, accordingly, the technological time.Originality. Due to the analysis of the force interaction of the ball elements at the final stage of the clutch operation, the dependencies for determining the elastic moment of the clutch at this stage of operation were obtained. The expressions for calculating the geometric parameters necessary to calculate its elastic moment were also obtained, which allows its estimation at any design parameters of the clutch. Practical value. The results obtained, together with other studies by the authors, are the source of information for modeling dynamic processes in drives with ball overrunning safety clutches, in particular, they make it possible to determine the load in such drives taking into account transient processes. Promising areas for further research are the analysis of the force interaction of the clutch parts at the beginning of a new cycle of its operation – the entry of the balls into engagement with the subsequent grooves of the outer half-clutch, as well as experimental studies of drives with the developed clutchs.

MODELING OF PRESSURE IN WRITING AND THE POSSIBILITY OF EVALUATING THE PRESSURE CHARACTERISTICS OF HANDWRITING

The article considers a physical-and-mechanical model of the writing process using a writing device with a ball element. The purpose of developing this model is to develop the theory of pressure in judicial handwriting, as well as to evaluate the pressure characteristics of handwriting, which are manifested primarily in the width and depth of handwritten strokes. At the same time, it is concluded that it is necessary to study handwriting objects from the perspective of their three-dimensionality, since it is the pressing characteristics of handwriting in this three-dimensionality that manifest themselves and allow for the further development of three-dimensional models of the writing process and the use of appropriate tools (technologies) to increase the reliability and objectivity of expert conclusions in the production of forensic handwriting examinations. The development of a physical-and-mechanical model reflecting the writing process is a very urgent task in judicial handwriting, since writing devices with a ball element (ballpoint pens, gel pens, roller pens) are currently used in writing much more often than others. The author offers a new definition of the concept of "pressure when writing", which takes into account both the physics of the writing process and its result according to the theory of trace formation adopted in traceology. He also demonstrated examples of calculating the pressure parameters manifested in the relief of handwritten strokes, outlined new approaches to the analysis and evaluation of the pressure characteristics of handwriting.

Analytical investigation of a new approach to calculation for effective length of the rolling element used in closed end needle roller bearings of driveshaft

The presence of the oscillating motion in a mechanical system, is vital in terms of the service life. Because the machine elements are under effect of fatigue due to the oscillating motion. The service life of the bearings which are in the forefront among the machine elements subjected to oscillating motion, can be calculated via an equation that depends on several variables, one of which is basic dynamic load rating (C). In this context, basic dynamic load rating (C) is one of the most important factors on estimating the service life.
 One of where bearing applications used in, is universal joint of driveshaft. A bearing on a universal joint consists of needle roller elements having larger contact area compared to the ball elements. Universal joint bearing is mounted in a bore on a component called yoke part, and so yoke part supports the bearing. In the calculation of basic dynamic load rating for universal joint bearing, effective length of the rolling element is the key factor. In this paper, a new approach to determine the effective length of rolling element used in closed end needle roller bearings of driveshaft has been investigated analytically and the effect of the said approach on the basic dynamic load rating and bearing life has been revealed in terms of ISO 281.

Comparative study of bearing wear in spindle system at different working conditions

In order to analyze the bearing wear in the spindle system considering different speed and load conditions, a four-bearing spindle system was investigated. Two different working conditions, Case I and Case II, are considered. Case I condition has lower spindle speed and higher external loads and preload than Case II condition. Based on Archard model, a new wear depth model of angular contact ball bearing is presented which takes into account the influence of lubrication on bearing wear. The wear depths of inner and outer raceways for angular contact ball bearings are calculated based on the motion parameters and contact parameters of ball elements which are obtained by spindle system model. The effects of spindle speed, angular misalignment, external load and surface roughness on the wear depths of bearings are comparatively studied. Increasing spindle speed at Case I condition can significantly increase bearing wear. Angular misalignment may be beneficial to individual bearing, but overall, no angular misalignment is the most beneficial to spindle system. The change rate of wear depth of bearing raceway with external loads at Case I condition is much greater than that at Case II condition. The surface roughness can significantly affect the bearing wear in the spindle system, especially at Case I condition.

ГИДРАВЛИЧЕСКОЕ СОПРОТИВЛЕНИЕ КОМБИНИРОВАННОЙ ОДНОПОТОЧНОЙ СИТЧАТОЙ ТАРЕЛКИ С ПОДВИЖНОЙ ШАРОВОЙ НАСАДКОЙ

The report presents the method of experiments and the results of the study of the 
 hydrodynamics of the gas-liquid system on a strainer one-threaded plate with a movable ball pack
 with different density of ball elements.

Daugavet- and delta-points in Banach spaces with unconditional bases

We study the existence of Daugavet- and delta-points in the unit sphere of Banach spaces with a 1 1 -unconditional basis. A norm one element x x in a Banach space is a Daugavet-point (resp. delta-point) if every element in the unit ball (resp. x x itself) is in the closed convex hull of unit ball elements that are almost at distance 2 2 from x x . A Banach space has the Daugavet property (resp. diametral local diameter two property) if and only if every norm one element is a Daugavet-point (resp. delta-point). It is well-known that a Banach space with the Daugavet property does not have an unconditional basis. Similarly spaces with the diametral local diameter two property do not have an unconditional basis with suppression unconditional constant strictly less than 2 2 . We show that no Banach space with a subsymmetric basis can have delta-points. In contrast we construct a Banach space with a 1 1 -unconditional basis with delta-points, but with no Daugavet-points, and a Banach space with a 1 1 -unconditional basis with a unit ball in which the Daugavet-points are weakly dense.

EFFECTS OF DESIGN PARAMETERS ON STATIC EQUIVALENT STRESS OF RADIAL ROLLING BEARINGS

The aim of this study is to theoretically investigate the effects of design parameters on the static equivalent stress of radial rolling bearings, such as the point contact case for ball bearings and line contact case for roller bearings. The contact pressure, contact area and von Misses stress of bearings are calculated based on geometrical parameters, material parameters and loading parameters by using the developed MATLAB program. To achieve this aim, both the maximum contact pressure pmax and Von Mises effective stress σVM are simulated with respect to design parameters such as varying ball and roller element diameters and varying ball and roller element elasticity modulus. For the point contact case and line contact case, it was concluded that increasing the diameter of ball and roller elements results in reducing the maximum contact pressure pmax Furthermore, increasing the elasticity modulus of the ball and roller elements results in increasing the maximum contact pressure σVM. Furthermore, increasing the elasticity modulus of the ball and roller element results in increasing the maximum contact pressure pmax and Von Mises effective stress σVM because of the decrease of contact area A. The determination of the diameter of the ball and roller elements and the selection of material are crucial and play an effective role during the design process. Therefore, bearing designers and manufacturers should make the bearing geometrical dimensions as large as possible and bearing material as elastic as possible. Furthermore, the stress-based static failure theory can also be used instead of the standard static load carrying capacity calculation. Moreover, Von Mises stress theory is also compatible with the finite element method.

Wear Analysis of Angular Contact Ball Bearing in Multiple-Bearing Spindle System Subjected to Uncertain Initial Angular Misalignment

Abstract The effects of the uncertainty of angular misalignment on the wear of angular contact ball bearings in the spindle system are investigated. The wear model of bearing raceways is derived based on the Archard model. The angular misalignment caused by mounting error is assumed to comply with normal distribution, Monte Carlo method is used to extract the angular misalignment sample. Based on the spindle system model, the spinning speed, pitch angle, and contact force of ball elements in each angular contact ball bearing are calculated. The wear depth of bearing raceways is analyzed. The results show that the uncertainty of the initial angular misalignment leads to significant dispersion of wear depth of ball bearings, but the dispersion degree is related to spindle speed, angular misalignment cases, and bearing mounting position. Increasing the spindle speed increases the wear depth but decreases the wear depth dispersion.

Analysis of a misalignment-insensitive spur gear transmission using a Rzeppa joint

The design of a novel gear system based on a Rzeppa joint internal interface is presented and analysed. The joint allows the transmission of torque loads while allowing real-time re-alignment of the gear to eliminate non-torque loads arising from misalignment. This gear, when part of a misaligned pair, is shown by means of quasi-static FE simulations to remain essentially under the same stress conditions, even when under considerable misalignment, and to outperform crowned gears. The trade-off is increased contact stress at the ball elements of the joint interface. In addition, the mesh stiffness for the conventional and the novel design are estimated, showing that the proposed design produces a lower but nearly constant stiffness throughout the mesh cycle.

ГИДРАВЛИЧЕСКОЕ СОПРОТИВЛЕНИЕ КОМБИНИРОВАННОЙ ДВУХПОТОЧНОЙ СИТЧАТОЙ ТАРЕЛКИ С ПОДВИЖНОЙ ШАРОВОЙ НАСАДКОЙ

In the aticle presents the method of experiments and the results of the study of the hydrodynamics of the gas-liquid system on a strainer two-threaded plate with a movable ball pack with different density of ball elements

ГИДРАВЛИЧЕСКОЕ СОПРОТИВЛЕНИЕ КОМБИНИРОВАННОЙ ДВУХПОТОЧНОЙ СИТЧАТОЙ ТАРЕЛКИ С ПОДВИЖНОЙ ШАРОВОЙ НАСАДКОЙ

The report presents the method of experiments and the results of the study of the hydrodynamics of the gas-liquid system on a strainer two-threaded plate with a movable ball pack with different density of ball elements

Fatigue Life Analysis of Ball Bearings and a Shaft System Considering the Combined Bearing Preload and Angular Misalignment

Bearing preload significantly affects the running performance of a shaft-bearing system including the fatigue life, wear, and stiffness. Due to the mounting error, the bearing rings are often angularly misaligned. The effects of the combined bearing preload and angular misalignment on the fatigue life of ball bearings and a shaft-bearing system are analyzed in this paper. The contact force distribution of angular contact ball bearings in the shaft-bearing system is investigated based on the system model. The system model includes the bearing model, and the shaft model is verified by comparing with the manufacturer’s manual and the results from other theoretical models, with the difference between the results from the present bearing model and manufacturer manual within 3%. The global optimization method is used to replace the Newton–Raphson algorithm to solve the ball elements’ displacements and friction coefficients, which improves the computation efficiency of the system model. The fatigue life of each bearing is evaluated with the consideration of the two preload methods and two angular misalignment cases. The fatigue life results show that the system life at the optimal angular misalignment is more than 1.5 times that without angular misalignment at the low preload value, and this ratio decreases as the preload value increases. The optimal angular misalignment of both the shaft-bearing system and the misaligned bearing is not always consistent, which depends on the preload value and bearing life. Both the constant-displacement preload and constant-force preload do not cause a significant difference in the highest system life. The different misaligned bearings can lead to different highest system lives as the preload value is low.

Porosity Prediction of Granular Materials through Discrete Element Method and Back Propagation Neural Network Algorithm

Granular materials are used directly or as the primary ingredients of the mixtures in industrial manufacturing, agricultural production and civil engineering. It has been a challenging task to compute the porosity of a granular material which contains a wide range of particle sizes or shapes. Against this background, this paper presents a newly developed method for the porosity prediction of granular materials through Discrete Element Modeling (DEM) and the Back Propagation Neural Network algorithm (BPNN). In DEM, ball elements were used to simulate particles in granular materials. According to the Chinese specifications, a total of 400 specimens in different gradations were built and compacted under the static pressure of 600 kPa. The porosity values of those specimens were recorded and applied to train the BPNN model. The primary parameters of the BPNN model were recommended for predicting the porosity of a granular material. Verification was performed by a self-designed experimental test and it was found that the prediction accuracy could reach 98%. Meanwhile, considering the influence of particle shape, a shape reduction factor was proposed to achieve the porosity reduction from sphere to real particle shape.

Study of the tribological properties of rolling element bearings under the effect of magnetic field

Purpose The purpose of this study was to examine the effect of the magnetic field to the friction coefficient in the rolling element bearings which exists in electric motors. Design/methodology/approach To achieve this, the test rig was modified to adjust the density of the magnetic flux applied to the rolling ball element bearing. Experiments were carried out in the magnetic field from 0 to 7.5 mTesla at magnetic flux density range from 15, 40 and 65 N constant loads. Also, its rotary speed selected as 100, 200, 400, 800 to 1200 rpm, respectively. Findings In the majority of the experiments, it was observed that the magnetic field affected the friction coefficient. This influence reduced the friction coefficient in some experimental conditions and increased in some of them. Originality/value In the literature, there are very few studies on the effect of magnetic flux density to the friction coefficient in these rolling element bearings. It has become clear that more studies have been conducted on the effects of the magnetic field and/or electrical current on bearing damages and failures. This aspect is a study with specificity.

Three-dimensional discrete element modeling of the irregularly shaped pebbles used in a truck escape ramp

The truck escape ramp is a clump of pebbles that is located alongside downgrades. As the pebbles are randomly placed in arrester beds, few studies have been conducted on simulation methods of the irregularly shaped pebbles. This paper proposed a pebble DEM model to analyze the micro-contact mechanism of the pebbles. Based on a polynomial algorithm, the 7th fit was selected and the coefficients of the edge curves were recorded. Second, the main view and left view were filled with preset numbers of ball elements. According to the ball element parameters, the ball elements were extended to three-dimensional models. Third, based on the edges of the main view and the top view, the ball element parameters were recalculated. Then, compression tests were conducted, and the key parameters of the pebble DEM model were calibrated. Based on the built pebble DEM model, compression tests were simulated with different pressing plate velocities and laying thicknesses. The results indicate that for increases in the pressing plate velocity, the contacting forces on the plate correspondingly increase, and this increase is linearly shaped. The results for different laying thicknesses indicate that for increases in the laying thickness, the contacting forces on the plate correspondingly decrease.

Macroscopic and microscopic simulation of silo granular flow based on improved multi-element model

In the PFC simulation of silo granular discharge, spherical particles were used in the traditional model, which could not accurately reflect macroscopic and mesoscopic mechanism during discharge of wheat, rice and other particles with non-spherical shapes. This research provides an improved multi-element model consisting of clump elements and ball elements. The model uses clump elements to simulate non-spherical grain particles and ball elements to simulate dust particles. The numerical simulation was carried out with the improved multi-element model, and the results are compared with the traditional simulation which uses the spherical ball elements and the experiment of grain discharge. It demonstrates that: (1) In terms of the normal wall pressure, the dynamic pressure fluctuation in flow with improved multi-element model is more gradual, and the discharge process lasts longer, the normal pressure simulation results are more accurate than the traditional model. (2) In terms of the meso-structure of the granular material, compared with traditional spherical ball model, the material packing porosity of the improved multi-element model decreases and the coordination number increases, which is denser and in consistent with the actual situation. (3) Particle shape would affect the meso-mechanical behavior of particles. The simulation results demonstrate that, compared with the traditional spherical ball model, the contact forces in the improved multi-element model increases, and the distribution of contact force chains is more uniform and denser; several arching force chains could be clearly seen in the improved multi-element model, which clearly reflects the dynamic change law of the instantaneous arch. The improved multi-element model established in this paper further improves the accuracy of simulation and reflects the dynamic changes of the normal pressure on the silo wall, granular material structure and meso-mechanical parameters during grain discharge.

Analysis of transient elastohydrodynamic lubrication of point contact subjected to sinusoidal dynamic loads

Vibration is inevitable from all machine elements operations since the load, surface velocities or contact radii change in time. In the case of a ball bearing application, the load changes as the ball elements rotate around the track. This change will be more rapidly when the external load changes. The vibrations induce a sinusoidal dynamic load working on the contact. On the other hand, the imperfect waviness on the contacting surfaces causes the vibration effects on the film thickness to become more pronounced. This paper numerically investigates the influence of the sinusoidal varying loads due to vibrations on the film thickness and pressure profile of the isothermal, elastohydrodynamically lubricated point contact with a wavy surface. For that purpose, a single contact between ball element and inner raceway is modeled as a contact between a spherical ball and a flat plate. The results reveal that the external sinusoidal dynamic load induces the modulations on the film thickness and pressure profile. The waviness on one contacting surface causes the changes in the EHL behaviors to become more pronounced.