Smooth Contact Research Articles

Vertical Dynamic Response of Rigid Circular Foundation in Multilayered Transversely Isotropic Poroelastic Half-Space

The influence of anisotropic properties and layering of saturated soils on dynamic response of a circular foundation under time-harmonic vertical loading is studied in this paper. The foundation is modeled as a rigid disk, with either permeable or impermeable and smooth contact surface, whereas a multilayered transversely isotropic poroelastic half-space is defined for the supporting soil. To investigate the dynamic interaction problem, a displacement and flow boundary condition at the contact surface is constituted by employing a discretization technique and the displacement influence functions, which are obtained from the exact stiffness matrix scheme, with the stiffness matrices being presented explicitly for the first time. A set of numerical results are presented to portray the effects of anisotropic and poroelastic properties, hydraulic boundary conditions, soil heterogeneity, and frequency of excitation on vertical dynamic response of rigid circular foundations. In addition, vertical vibrations of a ring foundation and a massive circular foundation are also investigated.

The contact mappings of a flat (2,3,5)-distribution

Let Ω and Ω′ be open subsets of a flat (2,3,5)-distribution. We show that a C1-smooth contact mapping f: Ω → Ω′ is a $$C^\infty$$ -smooth contact mapping. Ultimately, this is a consequence of the rigidity of the associated stratified Lie group. (The Tanaka prolongation of the Lie algebra is of finite type.) The conclusion is reached through a careful study of some differential identities satisfied by components of the Pansu derivative of a C1-smooth contact mapping.

Analytical model for meshing stiffness, load sharing, and transmission error for spur gears with profile modification under non-nominal load conditions

The loaded tooth deflections, manufacturing deviations, and assembly errors on spur gears induce a delay on the driven gear respect to the driving gear, which is called loaded transmission error. This delay causes an earlier start of contact outside the pressure line, resulting in a mesh-in impact, which is an important source of noise and vibrations. To avoid or mitigate this mesh-in impact, profile modifications on the driven tooth tip are frequently used. The additional gap due to the profile relief delays the effective start of contact, and a suitable amount of relief sets the mesh-in point back to the theoretical inner point of contact, which prevents the mesh-in impact and ensures a smooth contact. However, as the loaded transmission error depends on the transmitted load, a specific amount of relief will be suitable only for a specific input torque. For higher transmitted load mesh-in impact will occur again, while for lower transmitted load the effective contact ratio will be reduced due to an excessive delay of the start of contact. Therefore, under variable load conditions it is not possible to adjust the start of contact to the theoretical inner point of contact, so mesh-in impact, smooth contact and reduction of contact ratio may alternatively occur. In this paper, a simple analytical model for the meshing stiffness, load sharing ratio and transmission error is presented for spur gears with profile modification under non nominal -or variable- load conditions.

Sudden large-volume detachments of low-angle mountain glaciers – more frequent than thought?

Abstract. The detachment of large parts of low-angle mountain glaciers resulting in massive ice–rock avalanches have so far been believed to be a unique type of event, made known to the global scientific community first for the 2002 Kolka Glacier detachment, Caucasus Mountains, and then for the 2016 collapses of two glaciers in the Aru range, Tibet. Since 2016, several so-far unrecognized low-angle glacier detachments have been recognized and described, and new ones have occurred. In the current contribution, we compile, compare, and discuss 20 actual or suspected large-volume detachments of low-angle mountain glaciers at 10 different sites in the Caucasus, the Pamirs, Tibet, Altai, the North American Cordillera, and the Southern Andes. Many of the detachments reached volumes in the order of 10–100 million m3. The similarities and differences between the presented cases indicate that glacier detachments often involve a coincidental combination of factors related to the lowering of basal friction, high or increasing driving stresses, concentration of shear stress, or low resistance to exceed stability thresholds. Particularly soft glacier beds seem to be a common condition among the observed events as they offer smooth contact areas between the glacier and the underlying substrate and are prone to till-strength weakening and eventually basal failure under high pore-water pressure. Partially or fully thawed glacier bed conditions and the presence of liquid water could thus play an important role in the detachments. Surface slopes of the detached glaciers range between around 10∘ and 20∘. This may be low enough to enable the development of thick and thus large-volume glaciers while also being steep enough to allow critical driving stresses to build up. We construct a simple slab model to estimate ranges of glacier slope and width above which a glacier may be able to detach when extensively losing basal resistance. From this model we estimate that all the detachments described in this study occurred due to a basal shear stress reduction of more than 50 %. Most of the ice–rock avalanches resulting from the detachments in this study have a particularly low angle of reach, down to around 5∘, likely due to their high ice content and connected liquefaction potential, the availability of soft basal slurries, and large amounts of basal water, as well as the smooth topographic setting typical for glacial valleys. Low-angle glacier detachments combine elements and likely also physical processes of glacier surges and ice break-offs from steep glaciers. The surge-like temporal evolution ahead of several detachments and their geographic proximity to other surge-type glaciers indicate the glacier detachments investigated can be interpreted as endmembers of the continuum of surge-like glacier instabilities. Though rare, glacier detachments appear to be more frequent than commonly thought and disclose, despite local differences in conditions and precursory evolutions, the fundamental and critical potential of low-angle soft glacier beds to fail catastrophically.

Flexoskeleton Fingers: 3D Printed Reconfigurable Ridges Enabling Multi-Functional and Low-Cost Underactuated Grasping

In this letter, we present a design and fabrication framework for soft, underactuated grippers that utilize reconfigurable laminate layers for finger stiffness modulation. The grippers consist of internal flexoskeleton layers, which are hybrid soft-rigid structures composed of a flexible thermoplastic sheet with rigid structures 3D printed directly onto the flexible layer. The flexoskeleton structures are encased in an external silicone skin, which enables smooth and soft contact surfaces between the gripper and objects. We designed the flexoskeleton layers to be reconfigurable through layer sliding, which enables finger stiffness modulation by two methods: 1) continuum stiffness modulation through layer sliding to enable strong overlap gripping, and 2) locking and unlocking of flexoskeleton ridge structures that enable stable grasps without actuation. The gripper designs presented here are extremely easy to design and fabricate and present a template for future soft grippers.

Contact Stiffness Model of Joint Surface Considering Continuous Smooth Characteristics and Asperity Interaction

A new model to accurately obtain the contact stiffness of the mechanical joint surface is established, which satisfies the continuous smooth contact characteristics of the asperity and also considers the influence of the asperity interaction. In order to satisfy the continuous and smooth contact characteristics of the asperity, the interpolation interval of the Hermite polynomial function is improved to make the asperity contact stiffness curve smoothly transition in the elastic, elastoplastic and completely plastic stages. Further, the contact situation of the joint surface considering the asperity interaction is explored through micro-contact analysis and mechanism research. Finally, using statistical principles, the microscopic contact model is extended to the entire joint surface, and the contact stiffness model of the joint surface is established. The simulation results show that the asperity stiffness model satisfies the continuous smooth contact characteristics. Surface roughness is the main factor that affects the contact stiffness, and the influence of the asperity interaction cannot be ignored.

An effective method for calculating elasto-plastic contact pressure and contact patch size under elliptical, circular and line contact conditions

According to the Hertz's contact theory (HCT) and considering the strain hardening of materials, an effective calculation method is proposed for solving the elasto-plastic contact pressure and the contact patch size under arbitrary smooth and continuous contact conditions. Firstly, it is assumed that the outer and inner edges of the contact patch are elastic and elasto-plastic contact zones, respectively, the contact pressure in the elastic contact zone satisfies the HCT, while the contact pressure in the elasto-plastic contact zone is the superposition of a constant contact pressure and several small ellipsoidal distribution contact pressures. Then, the explicit expressions of contact patch size and contact pressure under the elasto-plastic elliptical, circular and line contact conditions are derived, respectively. Subsequently, the accuracy and applicability of the proposed method are evaluated by comparing the predicted results with the finite element simulations. Finally, the accuracy of the proposed method is further verified by comparing the predicted results with the typical results in literature. It is shown that the proposed method has high calculation accuracy, and the maximum relative errors are 9.32% for the elliptical contact, 4.61% for the circular contact and 11.84% for the line contact, respectively. Meanwhile, the proposed method can effectively predict the contact pressure distribution under the elasto-plastic elliptical, circular and line contacts, and shows a general applicability for different contact materials, contact-body's sizes and normal external loads, as well as for the elasto-plastic wheel-rail contact analysis.

A novel contact model for rough surfaces using piecewise linear interpolation and its application in gear wear

Wear is directly related to rough surface contact, and the accuracy of a wear prediction model depends on the accurate determination of contact pressure. In this work, a numerical model with high computational accuracy for rough surface contact is developed and applied to the wear prediction of spur gears. To acquire contact pressure, the integral equation that contact pressure should satisfy is discretized into a set of linear equations by piecewise linear interpolating contact pressure. Then, a gear wear model including rough surface contact is established. The proposed contact model is verified by comparing with smooth and rough surface contact, and the wear depths of a spur gear drive with geometry and pressure updates are analyzed. Result shows that a small roughness value among contact surfaces may cause a large change in contact pressure. The effects of main design parameters on gear wear are subsequently investigated. Gear wear is found to decrease with increased module and pressure angle but increases with increased transmission ratio and input torque. These findings indicate that reasonable parameter matching is beneficial to improving gear wear resistance.

Flexible Nanowire Cathode Membrane with Gradient Interfaces and Rapid Electron/Ion Transport Channels for Solid‐State Lithium Batteries

AbstractSolid‐state lithium batteries (SSLBs) have attracted more attention due to their improved safety and high energy density. Although numerous solid‐state electrolytes (SSEs) with high ionic conductivity have been frequently reported, poor solid–solid interfacial contact and interfacial chemical reactions around the cathode in SSLBs can hinder their practical application. Here, a gradient nanowire (NW) cathode is demonstrated for advanced interface engineering in SSLBs by a facile solvent evaporation process. In this unique gradient cathode membrane, one side surface with more ionic conductive polymer provides a smooth contact with SSE, while the other side surface with more electronic conductive NW/reduced graphene oxide composite provides rapid electron transport acting as a current collector. Furthermore, the inside NW cathode materials are uniformly coated by a solid polymer electrolyte and such a structure changes the point‐to‐point contact to a large‐area contact in the cathode, providing continuous channels for rapid electron/ion transport and improved mechanical strength. The effective interface engineering gives SSLBs enhanced structural stability and excellent electrochemical performance. The as‐obtained SSLBs can deliver 200 mAh g–1 capacity after 100 cycles at room temperature without obvious structural degradation. This novel design of NW‐based gradient cathodes demonstrates a promising strategy for solid–solid interface engineering in solid‐state lithium batteries.

Adhesion and friction in hard and soft contacts: theory and experiment

This paper is devoted to an analytical, numerical, and experimental analysis of adhesive contacts subjected to tangential motion. In particular, it addresses the phenomenon of instable, jerky movement of the boundary of the adhesive contact zone and its dependence on the surface roughness. We argue that the “adhesion instabilities” with instable movements of the contact boundary cause energy dissipation similarly to the elastic instabilities mechanism. This leads to different effective works of adhesion when the contact area expands and contracts. This effect is interpreted in terms of “friction” to the movement of the contact boundary. We consider two main contributions to friction: (a) boundary line contribution and (b) area contribution. In normal and rolling contacts, the only contribution is due to the boundary friction, while in sliding both contributions may be present. The boundary contribution prevails in very small, smooth, and hard contacts (as e.g., diamond-like-carbon (DLC) coatings), while the area contribution is prevailing in large soft contacts. Simulations suggest that the friction due to adhesion instabilities is governed by “Johnson parameter”. Experiments suggest that for soft bodies like rubber, the stresses in the contact area can be characterized by a constant critical value. Experiments were carried out using a setup allowing for observing the contact area with a camera placed under a soft transparent rubber layer. Soft contacts show a great variety of instabilities when sliding with low velocity — depending on the indentation depth and the shape of the contacting bodies. These instabilities can be classified as “microscopic” caused by the roughness or chemical inhomogeneity of the surfaces and “macroscopic” which appear also in smooth contacts. The latter may be related to interface waves which are observed in large contacts or at small indentation depths. Numerical simulations were performed using the Boundary Element Method (BEM).

Axisymmetric contact analysis of piezoelectric materials with surface effect

Based on the surface piezoelectricity theory, this article predicts the axisymmetric smooth contact of a piezoelectric half-space indented by a rigid insulated punch. In this theory, the surface effect is characterized with four material parameters: the surface elastic constant, surface residual stress, surface piezoelectric constant and surface dielectric constant. By applying Hankel integral transform, the fundamental solution for this axisymmetric contact problem is derived with the surface effect. Then, the normal contact stress, radial electric displacement and radial stress of the contact surface are solved numerically. Finally, the surface effects on the normal contact stress, radial electric displacement and radial stress are analyzed. It is found that the surface effect is a significant influencing factor on the axisymmetric contact behaviors of micro-/nano-scale piezoelectric materials.

Contact of the edges of the interphase cut on the arc of the circle between the isotropic plate and the closed elastic rib

In the conditions of the general flat stress state created by uniformly distributed effects of tension (compression) at infinity, the mixed contact problem for an infinite isotropic plate with a circular hole, which contour reinforced by a closed elastic rib in the presence of a symmetrical interfacial section at the boundary of their connection and the edges of cut in the process of deformation is smoothly contacted, is considered. The components of the deformation tensor (unit elongation, the angle of rotation of the normal and the curvature) at the point of the contour of the hole of the plate are represented by integral dependences on the contact forces. By modeling the reinforcement of a closed elastic rod of a stable rectangular cross of large curvature and using the basic equations of linear theory of curvilinear rods the mathematical model of problems is constructed in the form of systems of three singular integral equations with Hilbert cores to find contact forces between plates and rib. To determine the initial parameters of a closed static indeterminate rod, the conditions of unambiguous displacement and angles of rotation at the point of its axis and the equilibrium conditions are used. The approximate solution of the problem is constructed by the method of mechanical quadrature and collocations, which investigated the influence on the stress state of the plate and the reinforcing rib and on the size of the area of smooth contact of stiffness factor of rib.

非圆形水工衬砌隧洞与横观各向同性岩体在光滑接触下的解析分析

An analytical method for non-circular hydraulic lined tunnels in transversely isotropic rock mass was proposed, with the lining under the smooth contact condition with surrounding rock mass. Based on the complex variable theory, continuous conditions for stresses and displacements at the contact boundary and water pressure boundary condition at the lining free boundary were established. In view of the lining support delay effect and with the power series method, the analytical solution was acquired. Aimed at a horseshoe-shaped lined tunnel constructed in transversely isotropic rock mass with inclined structural face, the correctness of this method was validated by analytical check and numerical comparison. Distributions of stress and displacement at the contact boundary and lining free boundary under the effects of anisotropic property and water pressures were discussed.

A Continuous and Smooth Contact Stiffness Model for Mechanical Joint Surfaces

A Continuous and Smooth Contact Stiffness Model for Mechanical Joint Surfaces

Contact interaction of a predeformed plate which lies without friction on rigid base with a parabolic indenter

Within the framework of linearized formulation of a problem of the elasticity theory, the stress-strain state of a predeformed plate, which is modeled by a prestressed layer, is analyzed in the case of its smooth contact interaction with a rigid axisymmetric parabolic indenter. The dual integral equations of the problem are solved by representing the quested-for functions in the form of a partial series sum by the Bessel functions with unknown coefficients. Finite systems of linear algebraic equations are obtained for determination of these coefficients. The influence of the initial strains on the magnitude and features of the contact stresses and vertical displacements on the surface of the plate is analyzed for the case of compressible and incompressible solids. In order to illustrate the results, the cases of the Bartenev – Khazanovich and the harmonic-type potentials are addressed.

The execution of movement: a spinal affair.

In this tribute to Reggie Edgerton, I briefly review the spinal mechanisms that coordinate locomotion and the interaction between the different sensory mechanisms that help coordinate the locomotor movements and the central locomotor network. The step cycle has four distinct parts, the support phase, the lift off, the flexion phase, and, the most complex, the touch down, when the limb makes a smooth contact with ground again. Each of these phases is affected by different sensory mechanisms, which interact with the central network [central pattern generator (CPG)] generating the basic movements with its four components. Conversely, the CPG also gates the sensory reflex pathways, so that they are active only in a given phase of the step cycle, or even produces opposite effects in different parts of the step cycle. These different examples from mammals are most likely important also to consider for human locomotion and, in particular, in patients with spinal cord injury, partial or complete.

Pattern of Filling Up of Medical Certificate of Cause of Death at A Tertiary Care Hospital during Covid Pandemic: A Matter of Concern

Medical Certification of Cause of Death- MCCD, plays an important role in deciding the direction of public health programs, provide a feedback system for future implementation of health policies, health planning and management of epidemiological studies, vital statistics, medico-legal investigations, census studies, health research, assessment of effectiveness of public health programs. As Covid- 19 produces so much confusion into the mind of treating doctor as how to give cause of death in MCCD. Certification and classification and coding of death related to Covid-19 is essential for smooth contact tracing afterwards. Our study focused on the analysis of MCCD proformas filled up by residents and faculty members and common mistakes committed while filling it while treating the Covid patient at isolation wards. This is a retrospective, cross sectional study carried out at Covid-19 dedicated hospital associated with a Medical College situated in Rajasthan. The period of this study is three month of early Covid-19 pandemic time from 1st April 2020 to 30th June 2020, in which a total of 199 deaths were reported. We could study a total of 152 certificates (76.38%) out of total 199 deaths as in rest of cases, the MCCD was not attached as deceased was brought dead to hospital. The analytical result of study revealed some major errors like immediate cause of death was Covid-19 positive with cardiovascular arrest. The conclusion of our study highlights an urgent need for imparting extra efforts towards awareness, importance to undergraduates as well as postgraduate training. Also emphasis training of senior and junior faculty with other treating doctors. Suggestions to government for impose strict rules over clinician so that they know the importance of MCCD in pandemic time also.

Failure and mechanical behavior of transversely isotropic rock under compression-shear tests: Laboratory testing and numerical simulation

The failure and mechanical behavior of transversely isotropic rock are significantly affected by the original bedding planes. Until now, few studies have been performed to investigate the influence of the geometrical and mechanical parameters of the bedding planes on the fracture characteristics of transversely isotropic rocks under planar shear fracture loading conditions. For this purpose, experimental and numerical compression-shear tests on double-notched specimens are conducted to investigate the fracturing characteristics of transversely isotropic rock under planar shear fracture loading. The experimental study that focuses on the influence of bedding plane inclination on fracture load, fracture pattern and AE evolution, and six inclination angles is conducted in this study. Based on the flat joint contact model (for the rock matrix) and smooth joint contact model (for the original bedding plane) in PFC2D (particle flow code), the microscale fracturing process of transversely isotropic rock with different inclinations is simulated and analyzed. The results show that the inclination has an important influence on the fracture load and fracture pattern, and the maximum and minimum fracture loads are obtained for specimens with inclination angles of 30° and 60°, respectively. Moreover, the strength and spacing of the original bedding planes also play an important role in fracture loads. Higher bedding plane strength and wider bedding plane spacing result in higher fracture loads. In addition, with a moderate inclination angle, transversely isotropic rock with higher bedding plane strength tends to form cracks that cut through the rock matrix. However, with the decrease in the bedding plane strength, more fractures form along the bedding planes.

A case study on effective reduction in friction brake dust by adopting electric braking system

A good transportation facility plays important role in the growth of every country. The transportation networks are used to carry goods and passengers with the help of different vehicles. During the journey of every vehicle, it often undergoes braking operation due to transient road and traffic condition. To reduce the speed of the vehicle during braking the conventional brake system is used which consist of brake pad arrangements. The friction brake pads are rubbed against a smooth contact surface so that friction is generated to reduce the speed of the vehicle. Friction causes wear of brake pads and produce brake dust, which is freely released into the environment. Moreover, the produced brake dust particles are light in weight so that it freely floats in the air and inhaled by humans and animals. To investigate the effects of inhaled brake dust, several researchers conducted a clinical trial and found diseases related to the lungs. This article proposes a case study on an alternate solution for the friction brake system by adopting an electric brake system, which is free from dust emission. The outcome of the study shows an effective reduction in brake dust emission and possible risks associated with the health of human beings.

In Situ Investigation of Load-Dependent Nonlinearities in Tangential Stiffness and Damping of Spherical Contacts

Abstract Seemingly stationary (pre-sliding) interfaces between different materials, parts, and components are major sources of compliance and damping in structures. Classical pre-sliding contact models assume smooth elastic contact and predict that frictional slip leads to a well-defined set of stiffness and damping nonlinearities. However, reported data deviate from those predictions, and literature lacks a conclusive evidence leading to those deviations. In this work, the authors measure tangential stiffness and damping capacities inside a scanning electron microscope (SEM) while monitoring contacts between a rigid spherical probe and two materials (high-density polyethylene (HDPE) and polyurethane elastomer). Measured force, displacement, contact area, stiffness, and damping are then compared with predictions of classical models. In situ SEM images synchronized to the tangential force–displacement responses are utilized to relate the degree of plasticity and geometric alterations to stiffness and damping nonlinearities. In agreement with the classical models, increasing tangential loads cause softening in contacts under light normal preloads. In contrast, stiffness for HDPE increases with increasing tangential loads at heavy normal preloads due to plasticity and pileups over the contact. Material damping is prevalent for all loading cases in polyurethane samples thanks to nearly fully adhered contact, whereas for only light tangential loads in HDPE. With increasing tangential loading, specific damping capacity of HDPE contacts increases tenfold. This nonlinear increase is due to plastic shearing and frictional losses induced by tangential loading. Those findings suggest that predictive interface models should include geometric alterations of contact, plasticity, and material damping.