Rigid Ball Research Articles

Dynamic analysis of field-scale rockslides based on three-dimensional discontinuous smoothed particle hydrodynamics: A case study of Tangjiashan rockslide

To improve the understanding of the dynamic disastrous process of field-scale rockslides, a novel numerical approach, Three-dimensional Discontinuous Smoothed Particle Hydrodynamics (3DSPH), was originally developed. This method comprehensively captures sequential stages of crack initiation and propagation, formation of contacts, frictional slip, catastrophic slides of rock masses, and final deposition, which was verified by three benchmark tests including the bouncing test of rigid balls, block sliding test and unconfined compression test of layered rock specimens. The approach was subsequently employed in the case of the Tangjiashan rockslide blocking valley event with particular attention paid to the influence of layered rock structure on the sliding and deposition processes. Field survey, geomorphological analysis and laboratory test of rock specimens were conducted to determine fundamental geological conditions and parameters required by the numerical simulation. Finally, 3D rockslide simulations with different rock layer thickness and strength subject to seismicity were conducted. The duration of the actual Tangjiashan rockslide's valley-blocking event (approximately 60 s) and the deposition area derived from the numerical simulation closely align with the field investigation. The rockslide mode is characterized by an ‘en masse’ motion with a peak sliding velocity of approximately 35–37 m/s. This single numerical code systematically elucidated the authentic attributes of the sliding process of large-scale rockslides, and realistically captured the characteristics of preservation of layered features within the sliding mass and ‘high-speed and short-distance’ movements with fluidization. These insights offer a fresh perspective for understanding the dynamics of large-scale rockslides with complex geological structures and subsequent accumulation processes.

Straw movement and flow field in a crushing device based on CFD-DEM coupling with flexible hollow straw model

To accurately predict and evaluate the performance of the crushing device of no-till planter, it is strongly necessary to establish an accurate interaction model of the straw-crushing device coupling system. The traditional model has low prediction accuracy and cannot simulate the fracture characteristics of the straw during the operation of the crushing device due to the straw being usually regarded as a rigid body or a combination of rigid ball joints. In this paper, a breakable and flexible hollow straw model is first proposed and a CFD-DEM coupling model of the straw group-crushing device considering the effect of gas-solid two phase is also established. Afterwards, the corresponding verification experiments are conducted and the effect of working and structural parameters on the straw-throwing weight and crushing length is also analysed. It is demonstrated that the relative error between the simulation results and the experimental results for the straw crushing length is 7.7%, and the relative error for the straw-throwing weight is 7.1%, thereby verifying the correctness of the CFD-DEM model. Finally, the response surface method is also used to determine the optimal working and structural parameters of the crushing device and corresponding field tests verification is also conducted. Results indicate that the optimal parameter combination is as: the rotational speed of the crushing spindle is 2400 rpm, the inlet clearance is 30 mm and the starting point angle is 45°. Moreover, the crushing length after optimisation is 6.6% smaller than before optimisation, and the straw-throwing weight is increased by 11.5%.

Tunable rebound of millimeter-sized rigid balls by magnetic actuation of elastomer-based surface microstructures

A novel method for controlling the rebound behavior of small balls made of Al2O3 with a radius of 2.381 mm is presented. It uses different types of micro-structured surfaces of soft magnetoactive elastomers. These surfaces were fabricated via laser micromachining and include fully ablated surfaces as well as micrometer-sized lamellas with a fixed width of 90 µm, height of 250 µm and three different gap sizes (15, 60 and 105 µm). The lamellas can change their orientation from edge-on to face-on configuration according to the direction of the external magnetic field from a permanent magnet. The orientation of the external magnetic field significantly influences the rebound behavior of the balls, from a coefficient of restitution e of ≈0.5 to < 0.1. The highest relative change in the coefficient of restitution between zero field and face-on configuration of ≈80% is observed for lamellas with a gap of 60 µm. Other characteristics of the ball rebound such as the penetration depth into an Magnetoactive elastomer and the maximum deceleration are investigated as well. The proposed method does not require a constant power supply due to the use of permanent magnets. It may find novel applications in the field of impact engineering.

Numerical Point Contact Model of Mixed Elastohydrodynamic Lubrication for Transversely Isotropic Coating

Abstract Transverse isotropy, a typical property of coating providing protection or lubrication for transmission parts, is different from isotropy focused in most of previous research, catching increasing attention in recent years. This study aims to make the lubricating contact behavior of transversely isotropic coating under different working conditions better understood, with the assistance of a proposed mixed elastohydrodynamic lubrication (EHL) model for a rigid ball in contact with transversely isotropic coating. Explicit analytical expressions of frequency response functions (FRFs) of the elastic field for transversely isotropic coating were derived, which could be used to work out surface/subsurface displacement and stress if surface pressure is known. The proposed EHL model for transversely isotropic coating was verified by comparing the film thickness and pressure distribution with those from literature by an uncoated model. Furthermore, the effects of coating elastic property, coating thickness, velocity, and load on lubrication performance and mechanical responses are investigated. In addition, the results under different coating parameters are also compared and discussed with those obtained by the Hamrock–Dowson equations to demonstrate the effectiveness of the latter. This investigation may provide a potential application for coating optimal design considering lubrication.

Study on the Friction Contact Model between a Rigid Ball and Rubber Surface with Various Rubber Materials: A Numerical Investigation

Study on the Friction Contact Model between a Rigid Ball and Rubber Surface with Various Rubber Materials: A Numerical Investigation

Impact Elastohydrodynamic Lubrication Analysis of Transversely Isotropic Materials in Point Contact

Abstract In the traditional elastohydrodynamic lubrication (EHL) field, surface elastic deformation is usually determined using an elastic half-space model for isotropic materials. However, this theory may be inefficient when applied to point contact problems involving inherently anisotropic materials, such as transversely isotropic (TI) materials. Accordingly, the present study proposes a method for solving the EHL point contact problem between a rigid ball and a TI substrate under impact loading using a direct-solving numerical method, in which the mechanical properties of the TI material are expressed in the form of a stiffness matrix. For comparison purposes, the TI material is also approximated as an isotropic material using Turner’s approximation method based on the equivalent modulus property of the material. It is found that the direct-solving method outperforms Turner’s approximation in interpreting the mechanical properties of the TI substrate. In addition, it is shown that the initial velocity of the rigid ball and the stiffness of the TI material (i.e., the transverse elastic modulus, longitudinal modulus, and shear modulus) have significant effects on the load, impact velocity, and acceleration of the ball; central pressure and film thickness of the lubricant; and deformation and von Mises stress of the TI substrate, during the impact process. Overall, the results show that the proposed EHL model provides a useful tool for solving impact-EHL problems involving TI materials.

Finite element analysis of ball burnishing: evolution of residual stresses and surface profile in Ti-6Al-7Nb alloy

In the present study, the effect of feed on the residual stress distribution and surface profile generated during the ball burnishing of titanium alloy (Ti-6Al-7Nb) was investigated using finite element simulation. The elastic-plastic material model with isotropic hardening was used for performing the simulations. The created finite element model containing a rigid ball and deformable specimen was optimized and validated using experimental data. It was observed that the effect of burnishing feed is significant on the surface profile compared to residual stresses. The maximum residual stress obtained during the simulation of the process was achieved for the burnishing feed of 0.2 mm. This confirmed the variation of residual stress when the burnishing feed is varied. Whereas the surface roughness was the least for the 0.05 mm burnishing feed which was due to uniform deformation of the surface during the process.

Asymptotic profile for the interaction of a rigid ball and an incompressible viscous fluid

In this paper, we study the large time behavior of the solutions of the Stokes fluid-solid system. We compute the asymptotic expansion of the solution for Lq integrable initial data U0. We show that the asymptotic profile of the solution is a linear combination of the Stokes fundamental solution for the data with extra condition |x|U0∈L1. We also show that L1 integrability of the solution is strongly related to the net force exerted by the fluid on the boundary of the solid.

Numerical investigation of ice plate fractures upon rigid ball impact

The fracture process and breaking capability of ice cover impacted by high-speed projectiles before underwater explosion is an urgent subject of scientific research in ice engineering applications. This paper presents the results of numerical simulations of the dynamic fracture behaviour induced by the impact of a small spherical projectile on an ice plate. The proposed 3D rate-dependent peridynamics model is validated by the dynamic ring Brazilian disc testing of ice specimens. Good agreements between the present model and the previous experiments are obtained in ice breaking processes and damage patterns of thin, medium and thick ice plates. Several cases are analysed and discussed in terms of various impact velocities, ice thicknesses, and boundary constraint conditions. The simulations identify detailed fracturing characteristics that are not observed in experiments, including the sequence and shape of crack propagation in a short time interval, the crater formation and the damage evolution along the thickness direction. The proposed peridynamics computational model provides new understanding of the potential of using penetrator–ice block impact tests to observe the evolution of complex brittle damage and reveal the failure mechanism.

Analysis of accuracy of pedicle screw placement in dysplastic pedicles in adolescent idiopathic scoliosis using the pedicle expansion technique with CT-based navigation

BackgroundThis study aimed to study the accuracy of pedicle screw (PS) insertion into dysplastic pedicles in adolescent idiopathic scoliosis (AIS) comparing cannulated screw using the pedicle expansion technique (PET) versus conventional technique. MethodsForty-two AIS patients with 766 PSs were evaluated. In total, 236 screws were inserted into dysplastic pedicles: 138 and 98 screws were inserted using the PET (PET group) and standard technique (conventional group), respectively. Both methods used CT-based navigation to determine the insertion point. In the PET, a rigid ball tip feeler was tapped with a mallet to create an insertion route, a guide wire was passed through the tap, the pedicle was enlarged, and then a cannulated PS with a diameter of 4.35 mm was inserted. Postoperative CT was used to compare the accuracy of PS insertion. ResultsIn total, 23/236 (9.7%) perforations occurred. Regarding overall perforation, there were six (4.3%) and 17 (17.3%) cases in the PET and conventional group, respectively (P = 0.008). In terms of medial perforation, the PET group (n = 2, 1.4%) was significantly better than the conventional group (n = 7, 7.1%) (P = 0.021). In terms of lateral perforation, the PET group (n = 4, 2.9%) was significantly better than conventional group (n = 10, 10.2%) (P = 0.030). Only grade 1 perforation had occurred in the PET group, whereas grades 2 and 3 perforation occurred in the conventional group. ConclusionUse of the PET with CT-based navigation significantly increased the accuracy and safety of PS insertion in dysplastic pedicles in AIS.

Time-Fractional Cattaneo-Type Thermoelastic Interior-Boundary Value Problem Within A Rigid Ball

The paper discusses the solution of an interior-boundary value problem of one-dimensional time-fractional Cattaneo-type heat conduction and its stress fields for a rigid ball. The interior value problem describes the dependence of the boundary conditions within the ball's inner plane at any instant with a prescribed temperature state, in contrast to the exterior value problem, which relates the known surface temperature to boundary conditions. A single-phase-lag equation with Caputo fractional derivatives is proposed to model the heat equation in a medium subjected to time-dependent physical boundary conditions. The application of the finite spherical Hankel and Laplace transform technique to heat conduction is discussed. The influence of the fractional-order parameter and the relaxation time is examined on the temperature fields and their related stresses. The findings show that the slower the thermal wave, the bigger the fractional-order setting, and the higher the period of relaxation, the slower the heat flux propagates.

Simulation of the dynamics of a flexible fiber in the swirling airflow in a nozzle containing cylindrical and divergent conical sections

Swirling airflow plays a key role in textile production processes. The structure and properties of a textile processed by utilizing swirling airflow depend to a large extent on the dynamics of the fibers in the flow. This work presents a numerical investigation of the dynamics of a flexible fiber in the tangentially injected swirling airflow in a nozzle containing cylindrical and divergent conical sections, which is frequently encountered during textile production. Simulation of the three-dimensional, transient, compressible and turbulent swirling airflow field in the nozzle is first conducted. A model for the particle-level simulation of a flexible fiber in a wall-bounded flow is consequently adopted for studying the fiber motion in the nozzle. This model assumes the fiber to be composed of several massless elastic rods connected by rigid ball–socket joints where various forces and torques are exerted. The stretching, bending and twisting deformations of the fiber as well as the fiber–wall collision can all be modeled. The motional characteristics of the flexible fiber can be obtained by solving the translational and rotational equations for all the ball–socket joints in the fiber model. Based on the model, the effects of two process and nozzle geometric parameters – the nozzle pressure and radial position of the injectors – on the fiber motion are studied. The results show that the model and methods presented in this work can provide effective and useful insights into the dynamics of flexible fiber in the swirling airflow field inside complex-structured nozzles employed in the textile production processes.

Waves in the Earth’s core. III. A perturbative approach to quasi-free-decay modes

We consider the canonical problem of magnetic field decay in an electrically conducting fluid ball. The problem is closely allied to the problem of the decay modes of a rigid ball, and the spatial form of the eigenmodes survives largely intact. The decaying but oscillatory behaviour of the new fluid eigenmodes first discovered by Schmitt a decade ago (and named quasi-free-decay (QFD) modes) is deduced by application of perturbation methods to the case of rapid rotation and a static applied background magnetic field that is uniform and axial. Some, but not all, of the rigid-case poloidal eigenmodes share decay rates with other toroidal modes, necessitating the use of both degenerate and non-degenerate perturbation theory within this paper. The perturbation theory is developed in terms of the Elsasser number Λ (measuring the competition between Coriolis and Lorentz forces), and the analytic results are in striking accord with numerical calculations even when Λ is of O ( 1 ) . We find linear scaling of the QFD eigenfrequency with Λ and small changes in the decay rate that scale with Λ 2 . Although the modes are overdamped (quality factor Q &lt; 1 ), they are not strongly overdamped when the applied field is strong Λ ∼ 1 .

Self-Myofascial Release of the Foot Plantar Surface: The Effects of a Single Exercise Session on the Posterior Muscular Chain Flexibility after One Hour.

This study evaluated the effects of a single exercise session of Self-Myofascial Release (SMR) on the posterior muscular chain flexibility after one hour from the intervention. Thirty-six participants performed SMR using a rigid ball under the surface of both feet. Participants were tested with the Sit and Reach (S&R) test at four different times: before (T0), immediately after (T1), 30 (T2), and 60 (T3) minutes after the SMR intervention. The sample (n = 36) was categorized into three groups: (1) flexible, (2) average, and (3) stiff, based on the flexibility level at T0 (S&R values of &gt;10 cm, &gt;0 but &lt;10 cm and &lt;0 cm, respectively). For the whole sample, we detected significant improvements in the S&R test between the T1, T2, and T3 compared to T0. The stiff group showed a significant (p &lt; 0.05) improvement between T1-T2 and T1-T3. Results were similar between the average group and the whole sample. The flexible group did not show any significant difference (p &gt; 0.05) over time. In conclusion, this investigation demonstrated that an SMR session of both feet was able to increase posterior muscular chain flexibility up to one hour after intervention. Considering that a standard training session generally lasts one hour, our study can help professionals take advantage of SMR effects for the entire training period. Furthermore, our results also demonstrate that physical exercise practitioners should also assess individuals' flexibility before training, as the SMR procedure used in this work does not seem necessary in flexible individuals.

振動台実験による剛体球式感震器搭載ガスメーターの地震応答時における遮断特性の評価

Following earthquakes, it is essential to immediately assess the damage sustained in buildings and make judgments about the safety of their reoccupation. As instrumenting buildings with accelerometers is expensive, damage assessments are primarily done by entering the building and performing visual observations. As an alternative, the emergency gas shut-off feature available in gas meters installed in buildings is considered as a potentially effective indicator for identifying damage in structures. In this study, the commonly used gas meters equipped with `rigid ball type seismic sensor' are subjected to earthquake demands via shake-table testing to evaluate the shut-off characteristics.

Directional touch sensing for stiffness singularity search in an object using microfinger with tactile sensor.

Palpation is widely used as the initial medical diagnosis. Integration of micro tactile sensors and artificial muscles enables a soft microfinger for active touch sensing using its bending actuation. Active touch sensing by pushing-in motion of microfinger enables to evaluate stiffness distribution on an elastic object. Due to its compactness, the microfinger can enter a narrow space, such as gastrointestinal and abdominal spaces in a body. However, a microfinger can only touch and sense limited points. We aim at efficient method for searching a stiffness singular part in an elastic object by the directional touch sensing of a microfinger. This study presents a microfinger for active touch sensing using bending and push-in actuation and proposes an algorithm utilizing directivity in touch sensing by a microfinger for efficient localization of the stiffness singular part in an object. A gelatin block structure with a small rigid ball was prepared and touch sensed by the microfinger. Consequently, the position of the buried rigid ball could be efficiently identified based on the proposed algorithm. This result implies that the proposed method has potential applications in endoscopic medical diagnosis, particularly in identifying tumor positions.

An improved Smoothed Particle Hydrodynamics (SPH) method for modelling the cracking processes of teeth and its applications

The present work aims to propose a meshless method to establish the tooth meso-structures and model the tooth fracturing processes as well as investigate the influencing factors that affect the dental mechanical properties. To this end, the traditional kernel function in the SPH method has been improved by introducing a fracture mark ξ to realize the progressive failure processes of teeth; The “Particle Searching Method” has been proposed, which can realize the establishments of microstructures of teeth such as enamel, dentine, pulp, PDL and alvedar bones. The Weibull function is introduced to represent the heterogeneity of teeth, which can realize the random distribution characteristics of dental mechanical parameters. The simulation results of homogeneous and heterogeneous teeth show that the failure mode changes from tensile splitting (homogeneous) to shear failure (heterogeneous). Meanwhile, the fracture networks become more complex, and the failure stress decreases sharply. The cuspal angles also have a great impact on the teeth fracture characteristics. The failure modes changes from tensile splitting of the enamel tip to the cracking from the contact points between the enamel and the rigid ball; Different fssural morphologies have little influences on the teeth failure characteristics. The research results can provide some references for the applications of SPH method into biomechanical simulations such as teeth failure. Meanwhile, it can also provide some guidance for the understandings of the internal mechanisms of teeth fracture processes, the diagnosis and treatments of clinical diseased teeth as well as the design of bionic teeth materials.

Photoinduced Drude weights critically enhanced by charge fluctuations in a one-dimensional Mott insulator

This Letter theoretically validated that the $\ensuremath{\omega}=0$ component of a photoexcited Drude peak in one-dimensional Mott insulators is nonzero only when a finite amount of charge fluctuations is included. Here, we define charge fluctuations as annihilations and creations of photoexcited elementary particles, that are, holons (Hs) and doublons (Ds). In contrast, when the electron on-site repulsion, $U$, is infinite, such fluctuations are completely suppressed, and the H and D behave, such as rigid balls, leading to a vanishing $\ensuremath{\omega}=0$ component. Such behaviors inspire us to name them as ``quantum clackers.'' Moreover, we demonstrated that the effective broadenings of the finite-frequency components of the Drude peak are affected by charge fluctuations and carrier density. Finally, we discovered that such broadenings can be estimated using the group velocity of the relative motion of an H and a D as would be predicted from a colliding picture of the two particles.

Performance Evaluation of Different Coating Materials in Delamination for Micro-Milling Applications on High-Speed Steel Substrate.

The objective of the present work is to carry out analytical and finite element analysis for commonly used coating materials for micro-milling applications on high-speed steel substrate and evaluate the effects of different parameters. Four different coating materials were selected for micro-milling applications: titanium nitride (TiN), diamond-like carbon (DLC), aluminium titanium nitride (AlTiN) and titanium silicon nitride (TiSiN). A 3D finite element model of coating and substrate assembly was developed in Abaqus to find the Hertzian normal stress when subjected to normal load of 4 N, applied with the help of a rigid ball. The radius of the rigid ball was 200 µm. For all the coating materials, the length was 3 mm, the width was 1 mm, and the thickness was 3 µm. For the high-speed steel substrate, the length was 3 mm, the width was 1 mm, and the thickness was 50 µm. Along the length and width, coating and substrate both were divided into 26 equal parts. The deformation behaviour of all the coating materials was considered as linear–elastic and that of the substrate was characterized as elastic–plastic. The maximum normal stress developed in the FEA model was 12,109 MPa. The variation of the FEA result from the analytical result (i.e., 12,435.97 MPa is 2.63%) which is acceptable. This confirms that the FEA model of coating–substrate assembly is acceptable. The results shows that the TiSiN coating shows least plastic equivalent strain in the substrate, which serves the purpose of protecting the substrate from plastic deformation and the TiSiN of 3 micron thickness is the most optimum coating thickness for micro-milling applications.

Finishing of micro-aspheric tungsten carbide mold using small viscoelastic tool

Tungsten carbide is widely used as the material of replication mold to produce small aspheric optics, and the polishing process determines the precision of these molds. However, for micro-aspheric tungsten carbide mold, the existing polishing methods are difficult to realize the form error modification during a polishing process due to the polishing tool is always larger than small mold. Therefore, a polishing tool using polyester fiber cloth to wrap small-size rigid ball is used in this paper. In order to predict the tool influence function (TIF) of this polishing tool, a series of theoretical analysis and experimental verification are carried out in this paper. Firstly, by analyzing the structural and viscoelastic characteristics of the fiber cloth, the pressure distribution in the polishing contact area is determined. And the polishing speed distribution is obtained by analyzing the kinematic movement of polishing tool; Then, combined with Preston equation, the TIF is derived; Afterward, through a series of single point polishing experiments, it is verified that the volume error between the theoretical removal model and the experimental removal is less than 6.9% when the polishing pressure is low; Finally, the TIF is applied to the form error corrective polishing of small size symmetric aspheric tungsten carbide mold. After a form error corrective polishing test, the PV value (peak to valley) of form error is decreased from 0.268 to 0.083 μm, which verifies the effectiveness of this polishing method for small size tungsten carbide mold in form error correction.