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Transverse galloping is a type of flow-induced vibration (FIV) that leads to critical design considerations for engineering structures. A purely nonlinear energy sink (NES) composed of a ball free to rotate in a circular track experimentally mitigated the galloping of a square in a previous study. The current study introduces a model for simulating the dynamics of the square prism coupled with a ball-in-track (BIT) NES and predicting the system behaviour at high flow speeds beyond the limits of the previously presented experiments. Numerical simulations employ the fitting of experimental data as inputs to define parameters. Wind tunnel static experiments provide the galloping force coefficient [[EQUATION]] relative to the prism angle of attack. Additionally, free rotation tests allow evaluating the ball damping coefficient [[EQUATION]] as a function of its mass and the NES track radius. The result of the rotation tests provides a critical angular speed beyond which the ball damping increases non-linearly. We point out the damping variation as an advantage of the BIT-NES; less damping at low angular velocities helps the ball start its rotation, while relatively large damping at higher speeds dissipates more energy from the vibrating system. Numerical results exhibit four response modes for the NES; oscillatory at low flow speeds, intermittent within a small range of higher flow speeds, rotational at higher flow speeds, and ineffective regime at flow speeds out of the NES effective range. Modelling the primary mass as a parametric excitation source for the NES provides an analytical estimation of the boundary between the oscillatory and intermittent regimes. Furthermore, we advance an analytical analysis of the power flow across the integrated prism-NES system to explain the NES behaviour and predict the limit of its effective range.

Ball-end milling cutters are one of the most widely used cutters in the automotive, aerospace, die and machine parts industries. In addition, milling chatter will reduce the surface quality and production efficiency, resulting in noise. It is particularly important to model the cutting force and analyze the flutter stability of ball-end milling cutters. In this paper, a simplified milling force model of ball-end milling cutter with three degrees of freedom was established based on Merchant bevel cutting theory. The model simplified the milling force coefficient. The expressions of instantaneous milling area considering the vibration displacements in X, Y and Z directions were derived. The nonlinear dynamic cutting force model of ball-end milling cutter with three degrees of freedom was established. The nonlinear chatter vibration mechanical model of ball-end milling cutter with three degrees of freedom was established by introducing the time delay term, the stability analysis is carried out by time domain simulation. The proposed models were experimentally verified.

Distribution power flow (DPF) and distribution generation (DG) placement are important problems in modern distribution systems (DSs). The DPF problem is modelled as an optimization problem of minimizing the node power mismatches, while considering the corrections of node voltages as solution variables. The node locations and DG ratings of DG placement (DGP) problem are considered as optimization parameters with an objective of minimizing the network loss (NL). The soccer game optimization (SGO) models the movements of soccer game players by "move-off" and "move-forward" phases, and has the drawback of performing simple arithmetic average for representing random stochastic movements of players during its "move-forward" phase. This paper endeavours to first remodel the move-forward phase by adapting Levy Flight mechanism to simulate the random jumping action of players to a long distance in getting the ball and scoring a goal, and then develop new modified SGO (MSGO) based methods for solving the formulated DPF and DGP problems. The simulation study exhibited that the proposed DPF method is 751 and 666 times faster than the NR PF technique and the DGP method is able to save the NL by 65% and 69% for 33 and 69 node systems respectively.

New results about the influence of a small iron borided layer (~ 36 µm) obtained by the powder-pack boriding process (PPBP) and diffusion annealing post-process (DAP) were evaluated. Dry sliding wear tests on PPBP, PPBP + DAP and untreated AISI 1018 steel were performed under the pin-on-disc configuration, and balls of Al2O3 and WC were used as a counterpart at different sliding distances. Also, the contact pressures of the layer/substrate system were evaluated using the finite element model with the aid of the ABAQUS software. The results showed that the Al2O3 ball presented the major coupling (ball-disc), and the PPBP + DAP reduces the specific wear rate around ~ 304 times related to the untreated AISI 1018 steel to 500 m under severe sliding conditions.

In this study, residual stresses of cold-forged ball studs were investigated by the contour method with using widely available wire-Electro-Discharging Machine (wire-EDM) and Coordinate Measuring Machine (CMM). After the wire-EDM cutting, one of the steps of the contour method, it was revealed that the surface contour data was affected from the cutting step. Therefore, to increase the accuracy of the measured residual stresses, one of the ball studs were heat-treated to normalize residual stresses due to cold forging. The contour data of the heat-treated sample was subtracted from the as-forged surface contour to eliminate any cutting-induced artefacts. The final residual stress profiles suggested that the subtracting procedure minimized the cutting errors. In addition, a new classification approach for the cutting-induced errors for the contour method was introduced. According to final stress maps obtained by the contour method, it was revealed that high compressive residual stresses were obtained at the socket regions of the ball studs, as expected. Balancing tensile residual stresses were observed at the inner regions.

Ball-rolling dung beetles shape a portion of dung into a ball and roll it away from the dung pile for later burial and consumption. These beetles perform dances (rotations and pauses) atop their dung balls in order to choose an initial rolling direction and to correct their rolling direction (reorient). Previous mathematical modeling showed that dung beetles can use reorientation to move away from the dung pile more efficiently. In this work, we study if reorientation can help beetles avoid competition (i.e., avoid having their dung balls captured), and if so, under what circumstances? This is investigated by implementing a model with two different type of beetles, a roller with a dung ball and a searcher which seeks to capture that dung ball. We show that reorientation can help rollers avoid searchers in a wide range of conditions, but that there are some circumstances in which rolling without reorienting can be a beetle's optimal strategy. We also show that rollers can minimize the probability that their dung ball is captured without making precise measurements of the time interval between dances or the angular deviation for dances.

RoboCup is one of the greatest human endeavors to operationalize research in the field of robotics and artificial intelligence. RoboCup soccer simulation 3D (RoboCup3D) competition provide a great opportunity to work with humanoid robots without the need for hardware. One of the most important goals of the teams participating in RoboCup3D league is the ability to increase the number of shoots. The reason for this importance is that superiority over the opponent requires a powerful and precise shoot. The methods introduced for shooting so far are mostly based on Inverse Kinematics (IK) and point analysis. The assumption of these methods is that the positions of the robot and the ball is fixed. However, this is not always the case for shooting. In this paper, a shooting strategy is presented for situations where the robot is walking. Here, a curved path is designed to movement the robot towards the ball so that the robot will eventually have an optimal position to shoot. In general, the vision preceptor in RoboCup3D has noise. Hence, robot movement parameters such as speed and angle are more precisely adjusted by the Q-learning algorithm. Finally, when the robot is in the optimal position relative to the ball and the goal, the IK module is applied to the shooting strategy. Simulations and experiments prove the superiority of the proposed algorithm compared to most teams in RoboCupSoccer and Iran’s Open RoboCup3D leagues.

Ball-end cutters are widely used in industries of dies, molds, and aerospace, which have the problem of poor machined surface quality due to the low cutting speed near the tool-tip. With the increase in the complexity of parts, it will become more and more difficult to avoid the tool-tip participating in the cutting. In this paper, the velocity effect sensitivity of ball-end cutter is analyzed, and several key positions, including the intersection points of the CWE boundaries, are selected to describe the cutting speed in three dimensions. The relationships between the cutting speed of the critical points and important variables such as: machining inclination angle and the feed direction were investigated. The optimal range of feed direction is obtained when the tool-tip engages in the contact circle. The core aim of the feed direction selection is to make the tool engagement area in a high position by changing the feed direction, to avoid surface damage caused by ploughing and improve the quality of the machined surface. Finally, an experimental study was carried out, and the results corroborate the effectiveness of the selection method. In the experiment, it was also found that cutting-out from the cutter contact position can improve the surface quality in the directions of non-optimal range, and the milling force and chips shape will vary with the change of the feed direction.

This study developed machine learning (ML) models for predicting rock formation reactive forces experienced by a hydraulic shovel bucket during excavation. To do this, rock formation in the form of muckpile was modeled as granular ball elements in three-dimensional particle flow code (PFC) using linear bonding logic. A typical field-size hydraulic shovel bucket modelled in AutoCAD was used to excavate the rock formation and the three-dimensional shovel bucket resistive forces required to cut through the rock formation were measured and recorded. The experiments involved different muckpile height, bulk densities, repose angles, and average fragment size. Six ML algorithms, artificial neural network (ANN), K-nearest neighbor (KNN), linear, random forest (RF), regression tree (RT), and support vector machine (SVM), were evaluated on their ability to predict the shovel bucket resistive forces. The input variables used for the prediction of the resistive forces were the muckpile bulk density, angle of repose, height, and fragment size. The results showed that the ML techniques are useful and reliable methods of predicting rock formation resistive forces based on the rock formation properties. This research is a preliminary step towards developing reliable models for accurate prediction of excavation forces/torques which could potentially enhance hydraulic shovel process automation.

Steinitz’s theorem states that a graph G is the edge-graph of a 3-dimensional convex polyhedron if and only if, G is simple, plane and 3-connected. We prove an analogue of this theorem for ball polyhedra, that is, for intersections of finitely many unit balls in $$\mathbb {R}^3$$ R 3 .

The machining accuracy of a copper electrode gear (CEG), especially the pitch deviation of CEG, is affected by the wear of the ball end mill (BEM) with the increase of the length of milling path. Based on the error mapping principle, this work focuses on the influence of BEM wear on pitch deviation. In order to dynamically compensate the influence of the BEM wear on pitch deviation, a novel milling pitch deviation compensation model was proposed based on the formation mechanism and measurement principle of pitch deviation. To ensure the uniform wear at the milling edge of the BEM during the milling process, BEM wear was firstly copied to the pitch deviation according to the tooth-by-tooth milling strategy. Then, the BEM wear curve was fitted based on orthogonal experiments and multiple linear regression. According to the wear curve, an offline compensation method was adopted to compensate for the pitch deviation caused by BEM wear. In addition, the reverse compensation principle was used to compensate for the normal deviation of BEM milling path. Finally, the compensation model was verified by milling experiments. Pitch deviation met the requirements of Levels 4 $\sim $ 5 in GB/T 38192-2019. The model can be used to guide the milling process of CEG.

Load distribution in ball screws is a representation of the ball contact stress, and it is fundamental to understanding the behavior of these machine elements. This work aims to conduct a multi-variable analysis of the load distribution in ball screws. For this purpose, a numerical tool is developed for the generation and calculation of ball screw finite element (FE) models, which has been validated against the state of the art. This tool is based on the combination of an analytical contact model and the use of high-order FE models for the analysis of the load distribution of ball screws and stands out for its accuracy (less than 1% error against high-order FE models), adaptability, versatility (models are generated with more than 20 design variables and they can be introduced as components in larger models) and efficiency (being the computational time 1.25% of that of a high-order FE models) with respect to other existing models. Many different design variables (number of start threads, pitch, contact angle, ball size, slenderness and load arrangement) are studied in order to obtain a general characterization of the morphology of the load distribution in ball screws. Among them, the most influential variables on the load distribution and therefore on the structural behavior of ball screws are, load arrangement (with ratio r variations of up to 25% on the same ball screw) and slenderness (with ratio variations of up to 13% on ball screws with two turns of difference). The two most characteristic features, the non-uniformity at a local and global level are identified, along with as the possible causes of their appearance and the consequences that they may cause.

The use of nanoadditives in lubricants has gained much attention to the research community due to the enhancement of tribological properties and cooling capabilities. This paper studies the advantages of using a MQL (Minimum Quantity of Lubrication) system and nanoadditive in the manufacture of microneedle arrays in Ti6Al4V ELI alloy. Tungsten carbide ball nose tools with a cutting diameter of 200 µm were used in experimental tests. Surface and dimensional characterization was performed to evaluate the impact of a nanoadditive to a vegetable-based oil. Additionally, cutting forces and cutting edge radius (CER) were measured while needles were machined. Experimental tests confirmed that micro end milling with nanoadditives provide slightly better dimensional features and low cutting forces compared to oil. The performance of nanoadditives resulted in a reduction of surface roughness (~ 0.3 μm). Qualitative study of microneedles illustrated burr formation on needle surface manufactured without a nanoadditive solution. Results reveal an increment of CER using low feed rate values (2.0 µm/flute) while a reduction of CER was observed with feed rates up to 2.5 µm/flute. Our results indicated that the addition of nanoadditives to vegetable oil promotes a better product surface topography and cutting tool performance.

Previous studies have proposed that holding soft objects can increase expectations to be included in a Cyberball task. The present study investigated whether effects of holding soft objects on expectations are restricted to social contexts or can appear in non-social contexts. Sixty-six participants performed a social or non-social ball task, both modified versions of the Cyberball task. In the social ball task, participants were told that they would play a ball-tossing game with computer-generated players. In the non-social ball task, participants were told that they would take part in a judgement task. During the task, participants held either soft or hard cushions, and their electroencephalographic signals were recorded to evaluate the contingent negative variation (CNV), which is considered to reflect expectation and anticipation of an imperative stimulus. The results showed that participants who performed the social ball task exhibited larger late CNV when they held the soft cushion compared to when they held the hard cushion, whereas participants who performed the non-social ball task exhibited no such difference. The results indicate that holding soft objects increases expectations to be included only in social contexts.

Common 3-axis CNC milling machines are generally equipped with 2D tool radius compensation (2D-TRC), which can realize TRC function for the contours in three basic planes when flat end mills are used. The 2D-TRC function makes engineers to program according to the actual contour of a part, and avoids over-cut phenomenon. Unfortunately, the 2D-TRC is unsuitable for ball end mills (BEMs), especially in the situation of milling complex curves or surfaces. In this work, a new TRC named BEM-TRC is used for milling NURBS curve swept surfaces using BEMs based on 3-axis CNC milling machines. In BEM-TRC, the TRC of a BEM involves radial and axial compensation. The cutting point (CP), which is the tangent point between a BEM and a NURBS curve, is considered as a calculation basis point. After obtaining a CP on a NURBS curve using the equi-arc length bisection interpolation method, the cutter center point of a BEM is calculated through offsetting the CP the radius (r) distance of the BEM along its normal vector. Then the cutter location point of the BEM can be obtained according to the cutter center point. The CNC finishing program corresponding to the cutter location point can be obtained using Matlab software. The simulation based on VERICUT and machining based on a 3-axis milling machine verifies the effectiveness of the BEM-TRC. The over-cut phenomenon is avoided successfully when the BEM-TRC is used.

Ball burnishing is a finishing technique involving plastic deformation on the workpiece surface. In this paper, the influence of the ball burnishing operation on the average roughness, tensile properties, anisotropy and work hardening of a TRIP steel was analyzed. An experimental study of the effect of the ball burnishing process on uniaxial tensile specimens was conducted using the Response Surface Methodology (RSM) based on a 32 Factorial Design (FD). The effects of burnishing force (BF) and the number of tool passes (NP) on the average roughness (Ra), the yield stress (σY) and the percentage of elongation to fracture (% El) were evaluated. The quadratic regression models were obtained to predict Ra and σY with determination coefficients (R2) of 0.85 and 0.99, respectively. The results indicated that the ball burnishing process produces a maximum reduction of Ra of 81.7% (from 1.250 to 0.229μm). Also, it was observed that the ductility of the material increased in a 25% and the yield stress and work hardening can be substantially modified. Finally, it was found that by using the ball burnishing process, the planar anisotropy of the sheet can be reduced.

Ceramic balls are produced via powder metallurgy and compared to steel balls are preferred due to their special physical and mechanical properties. Ceramic balls can reach the desired surface finishing, sphericity, and diameter by finishing processes such as grinding, lapping, and polishing. By considering the length of time and high costs of the finishing process, creating an economic mechanism is of great importance in the use of ceramic balls. The present paper was conducted to investigate the eccentric lapping plates mechanism with eccentric V-grooves for ceramic balls lapping. This mechanism is proposed to increase the material removal rate (MRR) and to reduce the sphericity error of the ceramic balls. The effects of parameters including lower and upper lapping plate rotation speeds, the eccentricity of lapping plates, and lapping force were investigated on MRR, and the reduction of sphericity error. The kinematic analysis was performed to calculate the trajectory length and its distribution on the ball surface. Experimental tests were carried out to validate the kinematic analysis on the pre-sintered Al2O3 balls. The effects of the above-mentioned parameters on the lapping process were determined. The proposed mechanism provided an MRR of 0.766 mm/h; in this regard, sphericity error also reduced down 0.184 mm in 20 min.

This study used an alternating treatments embedded within a nonconcurrent multiple baseline across participants design to evaluate the effects of a stability ball chair on the on-task and in-seat behavior for three children with autism in a clinic setting. Results indicated increases for both in-seat and on-task behavior with the stability ball chair compared to a standard table chair, however, results varied across participants. On-task behavior had a greater increase across participants compared to in-seat behavior with the stability ball chair. Social validity results found that therapists had an overall positive view of stability ball chairs. This study provides clinicians with options for alternative seating to increase the on-task and in-seat behavior of children with autism. This study extends the use and evaluation of alternative seating, from typically studied settings and contexts, such as classrooms, to clinic settings with younger populations.

Demand for printed circuit board (PCB) recycling is increasing. To recover minor metals from PCB, the non-destructive detachment of electric parts is important, but has only recently begun to be investigated. To determine the optimal mechanical method for achieving such non-destructive detachment, a series of combined genetic algorithm (GA) and discrete element method (DEM) simulations were conducted, in the following manner: a breakable 2D PCB model was created by DEM; an impact ball with initial conditions and physical characteristics defined by a GA gene was driven into the PCB; the achievement of non-destructive detachment of an IC chip was assessed, and the fitness of the given gene was determined; genes were promoted for a hundred generations by the GA; and finally, the optimal non-destructive detachment conditions were determined. A notable feature of the combined GA-DEM program here employed was that various types of mechanical actions (e.g., blade stripping, hammer impact, and grinding) were able to be simultaneously investigated. The four different initial simulation conditions resulted in four different results; and among these, two considered suitable for actualization were investigated: stripping away the solder balls using a water jet and deforming the PCB through mechanical impact. With the water jet method, the detached IC chips were not destroyed, but universal parts detachment has not been achieved. With the mechanical impact method, IC chip detachment, probably caused by PCB deformation, was observed by a high-speed camera, which supported the simulation results.

In multi-axis ball end finish milling, the continuous change in cutting contact points produces complex wear overlapping zones. Moreover, each flute bears different actual cutting depths and contact points leading to inconsistent wear overlap distribution per tooth, which significantly affects the surface quality. Therefore, it is necessary to consider the wear overlap distribution per tooth to improve the surface roughness prediction accuracy. To address this issue, a time-varying surface roughness model is proposed considering wear overlap distribution per tooth. First, the model of wear overlap distribution per tooth considering the actual cutting depth and contact point is developed using the combined effects of the milling mechanism per tooth and the element wear model through the worn cutting edge trajectory. Then, the wear overlap distribution per tooth is embedded in the theoretical model of surface roughness through the geometric relationship of tool–workpiece engagement and milling radius model of worn cutter per flute under wear overlapping zones. Finally, the proposed method is validated through a case study. The testing results demonstrate that the wear overlap distribution per tooth and machined surface roughness could be forecasted exactly and effectively by the proposed method.

This paper studies automatic balancing of a flexible supported rotor with two disks by two ball balancers. Firstly, reduced dynamic descriptions of different components in the rotor are derived using a special method according to Lagrangian equation, based on which a general vibration model of the rotor system is then constructed. Secondly, equations governing frequency responses of the rotor are derived and working principles of the balls in the rotor are illustrated based on basic dynamic phenomena. Thirdly, an autonomous model of the rotor system is built with equations governing movement of the balls derived. Three equilibrium solutions are discovered whose dynamic characteristics are then studied using numerical bifurcation analysis method. Finally, locations of the balls at the steady state are observed using a high speed camera, and the capability of the two balancers for automatic balancing under different conditions is validated.

Ball surfaces play a crucial role in modeling 3D objects with varying thickness. In this paper, energy functionals for surface design are extended to Ball surfaces and the variational problem of finding the energy-minimizing Ball surface within the constraints imposed by the controls is investigated. Besides, owing to the excellent properties of Bernstein bases, we propose a computationally inexpensive algorithm for the construction of energy-minimizing Ball Bezier surfaces. Finally, an efficient design tool is provided for the construction of Cr continuous energy-minimizing blend surface from two disjoint Ball surfaces. The feasibility of the method is verified by several examples. By adjusting the weighted coefficients, different energy functionals are defined and thus Ball surfaces with different shapes and thickness can be obtained, achieving the deformable modeling of Ball surfaces.

The migration and distribution of lubricant oil in a rolling bearing strongly affect the elastohydrodynamic lubrication performance between the balls and rings. However, oil re-lubrication is highly dependent on the bearing design, which is different from the ball-on-disc model. This study directly observed the distribution of the lubricant film in a custom-made model-bearing rig, with an outer ring replaced by a glass ring to allow full optical access. The influence of the cage type and surface properties were presented. The physical origin of the re-lubrication mechanism, including capillary flow and mechanical redistribution, was discussed.

Wasserstein balls, which contain all probability measures within a pre-specified Wasserstein distance to a reference measure, have recently enjoyed wide popularity in the distributionally robust optimization and machine learning communities to formulate and solve data-driven optimization problems with rigorous statistical guarantees. In this technical note we prove that the Wasserstein ball is weakly compact under mild conditions, and we offer necessary and sufficient conditions for the existence of optimal solutions. We also characterize the sparsity of solutions if the Wasserstein ball is centred at a discrete reference measure. In comparison with the existing literature, which has proved similar results under different conditions, our proofs are self-contained and shorter, yet mathematically rigorous, and our necessary and sufficient conditions for the existence of optimal solutions are easily verifiable in practice.

This paper provides the dynamic model of an angular-contact ball bearing–elastic rotor system to study its dynamic characteristics when an asymmetric support mode is used. After defining global and local coordinate systems, necessary vectors (such as position, velocity, force and moment vector) are calculated according to the geometric relationship between each part (ball, cage and ring) of the bearing. The interactive forces between each part are obtained based on lubrication theory and Hertz contact theory. A typical rotor is discretized by finite element method (FEM) and each node of the rotor has 5 degrees of freedom (DOFs). Some constraint equations are built to form a coupled dynamic model of angular-contact ball bearing–elastic rotor system. The validity of this coupled model is verified by comparing the numerical results and experimental data. After analyzing the coupled model, it is found that the vibration spectrum of rotor includes the VC (varying compliance) frequencies of two bearings, the bending resonance frequency of rotor and the rotating frequency when the system has asymmetric ball bearings. Moreover, when the preloading forces of bearings increase, the support stiffness becomes larger and the rotor displacement decreases; moreover, the motions of balls and cage become more stable. Generally, the presented coupled model can be applied to analyze the vibration features of all parts in any ball bearing–rotor system comprehensively.

The machined surface topography of workpiece plays an important role in the performance and service life of workpiece. At present, the study of milling surface topography is mainly on 3-axis milling with ball end mill. Also, in 4/5-axis milling, surface topography analysis is mainly on the experimental data. In order to solve this problem, an analytical prediction model of milling surface topography is proposed, which can obtain the machined workpiece surface topography directly from cutting parameters, cutter location file, and workpiece surface geometry. The effects of cutting parameters on surface roughness are discussed, such as cutting velocity, feed speed, and lead angle. Different 4-axis milling experiment conditions are set up to validate the proposed model. The results show that the prediction results agree with experiment results. Also, this method can be used to predict the surface topography in five-axis milling and optimize the cutting parameters in the further.

Materials with high hardness are usually difficult to machine, and accomplishing precise and economical machining depends on all the cutting conditions. Appropriate tool geometry is one important aspect for the cutting process that can be optimized based on the machining parameters. In this study, the finite element simulation method was applied to analyze the effects of tool geometry on the cutting forces and tool temperature during the ball end milling of tool steel (AISI H13). Multi-objective optimization of the geometrical parameters was performed using the grey relational method, which gave a set of input parameters to obtain the minimum cutting forces and temperature. The findings of this work could be used as a basis for tool design. Experiments were conducted with mono-objective and multi-objective optimal geometries to validate the finite element analysis. The finite element and experimental results were both congruous with an error limit of 5%.

In numerical control machines, the thermal elongation of the ball screw influences the position accuracy. Different rotational speeds lead to different temperature changes at different positions in a ball screw system. In this paper, a new method is proposed to calculate the temperature rise of different positions when the ball screw is in the thermal equilibrium state. The thermal transmission of ball screws is analyzed, and the heat generation and transfer coefficient are calculated based on the laws of thermodynamics. The function between the temperature rise and position is built by solving the thermal equilibrium differential equations. The thermal elongation is obtained after the temperature rise is calculated. In order to prove the validity of this model, a series of detection tests are conducted to obtain the temperature rise of a ball screw and the thermal elongation under different rotational speeds. The experimental results show that the realistic temperature rise and the thermal elongation agree well with the theoretical values.

We develop a dual simplex-type algorithm for computing the smallest enclosing ball of a set of balls and other closely related problems. Our algorithm employs a pivoting scheme resembling the simplex method for linear programming, in which a sequence of exact curve searches is performed until a new dual feasible solution with a strictly smaller objective function value is found. We utilize the Cholesky factorization and procedures for updating it, yielding a numerically stable implementation of the algorithm. We show that our algorithm can efficiently solve instances of dimension 5000 with 100000 points, often within minutes.

The article describes the simulation results of an unbalanced rotary machine with an automatic ball balancer with a deep chamber (ABB-DC) based on a mathematical model of such a system. The ABB chamber has a cylindrical shape and is filled with balls that can move freely in general motion. The model takes into account mutual collisions between the balls, as well as between the balls and the chamber. The model also includes friction forces and rolling resistance. The comparison of simulation results performed with two different construction types of the chamber, classic single-layer drum (ABB-SC) and ABB-DC, confirmed the better efficiency of the ABB-DC in the optimal range of the number of balls. The machine body movement was limited to planar motion. The correctness of such a limitation has been verified by analyzing waveforms of reaction forces of constraints and their moments. Waveforms were divided into transient and steady states. The results of the analysis indicate the additional constraints do not significantly affect machine body movements. However, this might affect the ball arranging process in the ABB chamber. The paper also presents details of performing numerical simulations based on the developed mathematical model and numerical tests to determine the optimal integration time-step.

The magnetic moment of a spherical superconductor that is located on the axis of the external axisymmetric magnetic field is found. It is proved that the magnetic moment is completely determined by the value of the external field in the center of the ball.

The sliding-rolling mixed motion behavior degrades the ball screw’s precision at different levels. Based on the sliding-rolling mixed motion between ball and screw/nut raceway, the ball screw’s precision loss considering different given axial loading and rotational speed working conditions was investigated. Since creep and lubrication relate to sliding and rolling motion wear, the creep and lubrication characteristics are analyzed under different working conditions. Besides, the precision loss was calculated considering the sole influence of sliding behavior between ball and screw and compared with the results from other current models. Finally, research on precision loss owing to the sliding-rolling mixed motion behavior was realized under given working conditions, and suitable wear tests were carried out. The analytical results of precision loss are in good agreement with the experimental test conclusions, which is conducive to better predicting the law of precision loss in stable wear period.

Measuring and evaluating the geometric error of a linear axis periodically, is an essential operation in the day-to-day usage of a machine tool. In this paper, a system consisting of a novel one-dimension probe and a ball array is developed to fast estimate the geometric error a linear axis from the ball center deviations in three dimensions. The proposed 1D probe is assembled by an inductance micrometer and a simple fixture. Five measuring positions on the ball surface are selected to recognize the ball center offset caused by the geometric error. Then, an identification model is established to recognize the error at the ball center in the array. Moreover, a correction method is proposed to eliminate the installation error. It applies the least square method to form the virtual baseline by the measured ball centers, in order to eliminate the effect that resulted from the inaccuracy and the misalignment of the ball array during the manufacturing and setting, respectively. Then, the remaining part of the measured results is applied to evaluate the geometric error of the measured linear axis, including one positioning error and two straightness errors. Finally, a prototype system is developed to verify the correctness of the proposed 1D probe, while a measurement experiment is conducted on a machining center to verify the validity of the proposed method. The results indicate that the maximum absolute error among one positioning error and two straightness errors reach to 2.1 μm, 2.3 μm, and 1.6 μm, respectively, while the root mean square error, and the average absolute error are no more than 2.0 μm, when comparing with the results from the laser interferometer.

The machining surface quality has an important influence on the meshing performance and life of non-circular gear transmission. According to the meshing principle of non-circular gear transmission, the coordinate system of non-circular gear tooth surface was established, and the tooth surface equation of non-circular gear was obtained. Combined with the tooth surface equation of non-circular gear, the cutting edge motion model of ball end milling cutter was established, and the milling locus equation of cutting edge under multiple factors was deduced. The surface topography of the non-circular gear was obtained by simulation calculation, and the influence of interval feed and feed per revolution on the residual height was analyzed. The non-circular gear solid parts were processed by five-axis CNC milling with a ball end milling cutter, and surface topography measurement experiment was carried out. The experimental results and simulation results were compared and analyzed. The analysis results show that the actual machined surface topography has a high coincidence with the theoretical simulation surface topography, which verifies the rationality of the theoretical method. This study has a certain guiding significance to improve the surface quality of non-circular gear in ball end milling.

This paper takes an asymmetric support ball bearing-rotor system subjected by unbalanced force and parametric excitation (varying compliance) as the research object. Multi-modes of resonance such as natural frequency resonance region of each order, VC (varying compliance) frequency resonance region, the 1/2 sub-harmonic VC frequency resonance region, and quasi-periodic regions, and the nonlinear characteristics in these regions are analyzed. Besides, the effect of the number of balls of the ball bearing is also considered and the result shows that the parity of this parameter matters a lot. By introducing a definition of the absolute quasi-periodic frequency, the law of the occurrence of the quasi-periodic motion is demonstrated and the possible cause is given to some extent. The work provides a theoretical basis for clarifying the nonlinear characteristics of the bearing-rotor system and suppressing the nonlinear behavior of the system.

In this paper, a method is proposed for identification of 11 position-independent geometric errors (PIGEs) of five-axis machine tools with a tilting/rotary table via single-ball measurements and three-dimensional (3D) geometric sensitivity analysis. Eleven PIGEs were identified, including three squareness errors between three linear axes, two offset errors, and two squareness errors for the tilting/rotary axis. The approach uses a set-up of a ball and three circular measurements involving simultaneous control of two linear axes and a tilting/rotary axis. A 3D geometric sensitivity analysis is carried out to investigate the effects of the 11 PIGEs on each of the measurement’s paths and between the measurement paths. The particular measurement paths used allow the radius of the circular path at the first measurement, and the distance between the circular paths of the second and third measurements, to be increased for accurate identification of the 11 PIGEs. The proposed method was also used to derive root-sum-square values of sensitivity coefficients, and then applied to a commercial five-axis machine tool for experimental verification. It calculates the peak-to-valley values of the positional deviations in the x-, y-, and z-directions along the test paths as 152.1, 118.2, and 47.1 μm, respectively, without compensation for the identified PIGEs, and as 17.6, 15.0, and 11.4 μm, respectively, with compensation. The results confirm the validity of our proposed method.

The collision and wear caused by inevitable clearance in kinematic pair have an effect on the dynamic characteristics of the mechanism. Therefore, we established the dynamic model of a 3RSR (R is the revolute joint and S is the spherical joint) parallel mechanism with spherical joint clearance based on the modified Flores contact force model and the modified Coulomb friction model using Newton-Euler method. The standard quaternion was introduced in the constraint equation, and the four-order Runge-Kutta method was adopted to solve the 3RSR dynamic model. The simulation results were compared and analyzed with the numerical results. The geometrical parameters of the worn ball socket were solved based on the Archard wear model, and the geometrical reconstruction of the worn surface was carried out. The geometric reconstruction parameters were substituted into the dynamic model, which was to analyze the dynamic response of the 3RSR parallel mechanism with wear and spherical joint clearance. The simulation results show that the irregular wear occurs in the spherical joint with clearance under the presence of the impact and friction force. The long-term wear will increase the fluctuation of the contact force, thereby decreasing the movement stability of the mechanism.

One-Class Classification (OCC) is a supervised learning technique for classification whereby the classifier is obtained only by training the objects from the target class and identifying whether new observations belong to the class or not. In this paper, we propose a novel approach to OCC, which is based on optimal covering of the target objects by ‘good’ norm balls. The proposed classifier consists of the selected norm balls from an integer programming model where the finite norm ball candidates from the target objects are used. Computational experiments were carried out to examine the performance and characteristics of the proposed classifier using artificial and real data from the UCI Repository. The results showed that the proposed model was comparable to existing OCC methods in the comparison group. In addition, the proposed model demonstrated high sparsity leading to low testing burden and robustness to noises.

The Montney tight siltstone reservoir is a multi-stacked play, which covers a total area of 130,000 km2 along the Alberta–British Columbia border in Western Canada. Since the late 1990s, different fracturing methods and fluids have been tested in 4000-plus Montney wells to find the optimal fracturing method and fluid. The previous studies reviewing the performance of fracturing methods in Montney do not represent a holistic evaluation of these methods, owing to some limitations, including: (1) using a small sample size, (2) having a limited scope by focusing on a specific aspect of fracturing (method/fluid), (3) relying on data analytics approaches that offer limited subsurface insight, and (4) generating misleading results (e.g., on optimum fracturing method/fluid) through using disparate data that are unstructured and untrustworthy as a result of significant regional variations in true vertical depth (TVD), geological properties, fluid windows, completed lateral length, fracturing method/fluid/date, and drawdown rate management and choke size strategy. The present study eliminates these limitations by rigorously clustering 4000-plus Montney wells based on the TVD, fluid window, completed lateral length, fracturing method/fluid/date, and drawdown rate strategy to isolate the effect of each fracturing method by comparing each well’s production to that of its offsets, which use different fracturing methods but possess similar geology, fluid window, and TVD. With similar TVD, fracturing fluid, and completion date, wells completed with pinpoint fracturing method outperform their offsets completed with ball-and-seat and plug-and-perforate (PnP) fracturing methods. However, wells completed with ball-and-seat and PnP methods that outperform their offset pinpoint wells have either: (1) been fractured one to four years earlier than the pinpoint wells and/or (2) used energized oil-based fluid, hybrid fluid, and energized slickwater versus slickwater used in the pinpoint offsets. This suggests that the water-phase trapping is more severe in these pinpoint wells attributable to the use of slickwater. Previous studies often favored one specific fracturing method or fluid without highlighting these complex interplays between the type of fracturing method, fracturing fluid, completion date (regional depletion or well vintage), and the reservoir properties and hydrodynamics.

Ball-on-socket articulation is the major structural type of artificial joints. The insight on the mechanical and bio-tribological characteristics of this structure is important for designing both the device itself and its wear assessment regime. Two kinds of ball-on-socket structures were studied including a simplified general model and a real artificial cervical disc. The bio-tribological behaviors were evaluated by in vitro wear simulation method using four kinds of pairs with different combinations of structure, frictional material and testing duration under alternate motion of FE-AR (flexion extension and axial rotation) and LB-AR (lateral bending and axial rotation). In order to analyze the formation mechanism of representative wear characteristics, the mechanical behaviors were also studied by finite element analysis method. The results indicated that there were similar mechanical and bio-tribological characteristics for these two structures after about 9 MC (Million Cycles) tests. Under the axial load, it revealed more serious wear severity in the edge region than that in the central region for both convex polymer component and concave metal component, which may be due to much higher values of equivalent stress and equivalent elastic strain in the edge region than that in the central region. Under FE (flexion extension) or LB (lateral bending) motion, it showed common wide and curved wear grooves with ring distribution in the edge region for both ball component and nucleus pulposus component, which may be attributed to the higher equivalent stress and equivalent elastic strain at the limit position. It just indicated several sliding scratches for TC4 (Ti6Al4V alloy) metal component with an abrasive wear mechanism, while it revealed plastic deformation, surface cracks, sliding scratches and wear grooves for XPE (crosslinking polyethylene) polymer component with a mix of abrasive wear and adhesive wear mechanism. Hence, there was a strong correlation between structural design and bio-tribological characteristics for ball-on-socket prostheses.

Titanium alloy parts with a large inclined angle and thin-walled group holes exhibit low machining efficiency, poor position accuracy, and difficulties in the manufacturing of small gap grouped graphite electrodes. To achieve the high-efficiency and high-precision machining of such titanium alloy parts, in this study, we propose the electrical discharge machining (EDM) technology based on distributed group electrodes and the tool ball positioning method. Orthogonal process experiments were designed considering process parameters including the peak current, pulse width, duty cycle, and lifting cycle. A comprehensive and intuitive balance analysis method was used to determine the material removal rate, relative electrode loss, and surface roughness, as well as the optimal combination of the process parameters. We constructed the distributed group graphite electrodes and the positioning system of the tool ball, which significantly reduced the machining difficulty of traditional group electrodes and the replacement times of electrodes during machining, and improved the positioning accuracy of electrodes. The results showed that an optimal combination of the parameters could effectively improve the machining efficiency and reduce the electrode loss while ensuring the surface quality requirements. The above-mentioned methods can improve the machining efficiency of the titanium alloy parts with a large inclined angle and thin-walled group holes by more than 1.5 times and significantly reduced the machining accuracy error of repeated positioning.

Textured surfaces offer the potential to promote friction and wear reduction by increasing the hydrodynamic pressure, fluid uptake, or acting as oil or debris reservoirs. However, texturing techniques often require additional manufacturing steps and costs, thus frequently being not economically feasible for real engineering applications. This experimental study aims at applying a fast laser texturing technique on curved surfaces for obtaining superior tribological performances. A femtosecond pulsed laser (Ti:Sapphire) and direct laser interference patterning (with a solid-state Nd:YAG laser) were used for manufacturing dimple and groove patterns on curved steel surfaces (ball samples). Tribological tests were carried out under elasto-hydrodynamic lubricated contact conditions varying slide-roll ratio using a ball-on-disk configuration. Furthermore, a specific interferometry technique for rough surfaces was used to measure the film thickness of smooth and textured surfaces. Smooth steel samples were used to obtain data for the reference surface. The results showed that dimples promoted friction reduction (up to 20%) compared to the reference smooth specimens, whereas grooves generally caused less beneficial or detrimental effects. In addition, dimples promoted the formation of full film lubrication conditions at lower speeds. This study demonstrates how fast texturing techniques could potentially be used for improving the tribological performance of bearings as well as other mechanical components utilised in several engineering applications.

In the last decades, the automation process has improved humans’ daily life. As technology continues to evolve, software and machines are increasingly being used to automate everyday tasks that were once performed by humans. For instance, sports have already seen some use of wearable devices in activities involving monitoring and measurement of position speed and body parameters, for example, heart rate and maximal oxygen consumption (VO2). Despite that, a personal trainer is still necessary to catch athlete’s errors. Computer vision can be applied to this problem, helping athletes to improve their performances. Therefore, this work describes a low-cost computer vision algorithm to track a tennis ball’s vertical motion. The algorithm aims to determine the touch position and to record a picture of the moment for analysis. The method works by applying color filters and transformations combined with a support vector machine to accurately detect the line and ball positions. The ball position is tracked along with different pictures, and a mathematical model is used to estimate the ball trajectory and helping predict the touching instant. An Extended Kalman Filter is applied in this work to reduce measurement error and improve detection performance by predicting future positions for the ball. The ground line positions are determined based on a Hough transform to detect the tennis court lines. The results have shown excellent performance and technical feasibility of the method for deployment in low cost embedded computers.

In this study, the tribological performance of two FeB/Fe2B systems formed at the surface of an AISI 316L stainless steel was evaluated experimentally as well as numerically using the configuration rotatory pin-on-disk test, without lubricant and using a ball as a counterpart. The wear tests were carried out along a circular path under two applied loads of 5 and 10 N and a constant sliding distance. The wear coefficient was obtained by Archard’s model. Experimental results of the wear test exhibited that the FeB/Fe2B system with the thinner thickness developed more severe wear. The principal stresses and the maximum shear stress at the beginning and at the end of the pin-on-disk test were assessed by means of the finite element method. Mesh nonlinear adaptivity was used in the numerical model of the pin-on-disk test to fix mesh distortion caused by the surface wear. As the pin-on-disk test progressed and the material was removed, it caused a non-uniform contact pressure on the contact zone, which generated high stress at small areas of boride layers.

To ensure the stability of precision of the motorized spindle for five-axis machining center, the thermal error of five-axis machining center was investigated, and the temperature rise-thermal deformation model of a thin-wall ring type rotary elastomer was built on the basis of thermo-elastic property. Thus, a model of radial thermal error was con-structed. The relationship between radial error and axial error was also investigated in this paper and the total radial errors were gotten. In addition, the thermal error of the motorized spindle of five-axis machining center was measured by the ball bar in the experiment of thermal error. The motorized spindle total radial error was achieved by this experiment and radial total error analytical model. Finally, a BP neural network algorithm was introduced for thermal error prediction of five-axis machining center, and the precision of prediction of these models was compared and analyzed. The analysis shows that this method is practical and effective.

We study the infinite urn scheme when the balls are sequentially distributed over an infinite number of urns labeled 1,2,... so that the urn j at every draw gets a ball with probability $$p_j$$ p j , where $$\sum _j p_j=1$$ ∑ j p j = 1 . We prove functional central limit theorems for discrete time and the Poissonized version for the urn occupancies process, for the odd occupancy and for the missing mass processes extending the known non-functional central limit theorems.

Stability balls have become a common option for alternative seating in classrooms. While the social validity of stability ball classroom seating remains high among students and teachers, findings on the effectiveness of this alternative seating method are mixed. This is particularly true when the intent of the intervention is to increase student on-task behavior. This study examined the effects of stability ball seating on students’ on-task behavior in a general education setting, using a within-subjects repeated measures design. Researchers observed twenty-four third-grade students in a public-school classroom across three conditions: all chairs, all balls, or choice. Across observation days, the study controlled for time of day, teacher, and classroom environment. Results indicate students are on-task less frequently when sitting on a stability ball. Student reports on social validity replicated prior findings; students found the stability ball to be desirable and easy to use.

Position independent geometric errors (PIGEs) of rotary axes, which are caused by imperfections during assembly of machine tools, are proved to be one of the major error sources of a five-axis machine tool. In this paper, PIGEs’ characterization method through hybrid motion of linear-rotary axes using a double ball bar (DBB) is proposed. The coordinated motions involving the motion of a linear and rotary axes are designed, namely, the XC, YC, and ZB motion pairs. The comprehensive error model of the machine tool is established using the screw theory based on the machine tool topology. The asynchronization between the synthetized velocity of the spindle tool cup relative to the workpiece tool cup during the coordinated motions has been resolved based on optimal motion trajectories. The PIGEs are identified using the particle swarm optimization method and simulated using the comprehensive machine tool model. A compensation strategy of the identified errors is proposed using the machine inverse kinematics. The effectiveness of the proposed characterization method is proved by the compensation results.

This paper presents a novel method to identify the squareness errors of computer numerical control (CNC) machine tools based on double ball bar (DBB) measurements. A series of spherical S-shaped paths are proposed to measure the squareness errors, instead of the generally used circular detection paths since the presented method requires only one experimental setup, and three translation axes are linked, which is more convenient and comprehensive. In this article, the coordinate transformation method and the method for dividing experimental paths evenly are used to solve the asynchronization between actual motion and DBB sampling process. The experimental data is then combined with the product of exponential (POE) model to calculate the three CNC machine tool squareness errors and applied to a spherical spiral testing path with the compensation of the diagnosed errors. The effectiveness of the method is verified by comparing the experimental results before and after the compensation.