Complete Slip Research Articles

Avoiding self-loosening failure of bolted joints with numerical assessment of local contact state

Fatigue and rotational self-loosening are two most widespread reasons for failure of dynamically loaded bolted joints, especially due to external loading perpendicular to the bolt axis (transverse loading). More and more component systems show self-loosening in light weight design. The aim of this paper is to provide a numerical design method with finite element analysis for detecting and understanding of the self-loosening process at bolted joints and the influences of the preload generation for the residual shank torque in the numerical simulation. A three-dimensional finite element (FE) model is established to study details of the rotational self-loosening process. Such processes are characterized by either complete or localized slip at the screw head and thread contact surfaces. Detailed information is given about the modelling. The computational results of the numerical simulation are compared with experimental investigations of the cyclic transverse load–displacement behaviour. These show that rotational self-loosening can also occur for only localized slip without complete slipping at the head contact surface.

The 3-D Inviscid Limit Result Under Slip Boundary Conditions. A Negative Answer

We show that, in general, the solutions to the initial-boundary value problem for the Navier-Stokes equations under a widely adopted Navier-type slip boundary condition do not converge, as the viscosity goes to zero, to the solution of the Euler equations under the classical zero-flux boundary condition, and same smooth initial data, in any arbitrarily small neighborhood of the initial time. Convergence does not hold with respect to any space-topology which is sufficiently strong as to imply that the solution to the Euler equations inherits the complete slip type boundary condition. In our counter-example Ω is a sphere, and the initial data may be infinitely differentiable. The crucial point here is that the boundary is not flat. In fact (see Beirão da Veiga et al. in J Math Anal Appl 377:216–227, 2011) if $${\,\Omega = \mathbb R^3_+,}$$ convergence holds in $${C([0,T]; W^{k,p}(\mathbb R^3_+))}$$ , for arbitrarily large k and p. For this reason, the negative answer given here was not expected.

The Uniform Rugosity Effect

Relying on the effect of microscopic asperities, one can mathematically justify that viscous fluids adhere completely on the boundary of an impermeable domain. The ru-gosity effect accounts asymptotically for the transformation of complete slip boundary conditions on a rough surface in total adherence boundary conditions, as the amplitude of the rugosities vanishes. The decreasing rate (average velocity divided by the amplitude of the rugosities) computed on close flat layers is definitely influenced by the geometry. Recent results prove that this ratio has a uniform upper bound for certain geometries, like periodical and almost Lipschitz boundaries. The purpose of this paper is to prove that such a result holds for arbitrary (non-periodical) crystalline boundaries and general (non-smooth) periodical boundaries.

Evaluation of the influence of interface elements for structure - isolated footing - soil interaction analysis

In this study, two extreme cases of compatibility of the horizontal displacements between the foundation and soil are considered, for which the pressure and settlements of the isolated footings and member end actions in structural elements are obtained using the three dimensional models and numerical experiments. The first case considered is complete slip between foundation and soil, termed as the un-coupled analysis. In the second case of analysis, termed as the coupled analysis, complete welding is assumed of joints between the foundation and soil elements. The model and the corresponding computer program developed simulate these two extreme states of compatibility giving insight into the variation of horizontal displacements and horizontal stresses and their intricacies, for evaluation of the influence of using the interface elements in soil-structure interaction analysis of three dimensional multiscale structures supported by isolated footings.

The effective boundary conditions for vector fields on domains with rough boundaries: Applications to fluid mechanics

The Navier-Stokes system is studied on a family of domains with rough boundaries formed by oscillating riblets. Assuming the complete slip boundary conditions we identify the limit system, in particular, we show that the limit velocity field satisfies boundary conditions of a mixed type depending on the characteristic direction of the riblets.

Molecular structure, mechanical behavior and failure mechanism of the C-terminal cross-link domain in type I collagen

Collagen is a key constituent in structural materials found in biology, including bone, tendon, skin and blood vessels. Here we report a first molecular level model of an entire overlap region of a C-terminal cross-linked type I collagen assembly and carry out a nanomechanical characterization based on large-scale molecular dynamics simulation in explicit water solvent. Our results show that the deformation mechanism and strength of the structure are greatly affected by the presence of the cross-link, and by the specific loading condition of how the stretching is applied. We find that the presence of a cross-link results in greater strength during deformation as complete intermolecular slip is prevented, and thereby particularly affects larger deformation levels. Conversely, the lack of a cross-link results in the onset of intermolecular sliding during deformation and as a result an overall weaker structure is obtained. Through a detailed analysis of the distribution of deformation by calculating the molecular strain we show that the location of largest strains does not occur around the covalent bonding region, but is found in regions further away from this location. The insight developed from understanding collagenous materials from a fundamental molecular level upwards could play a role in advancing our understanding of physiological and disease states of connective tissues, and also enable the development of new scaffolding material for applications in regenerative medicine and biologically inspired materials.

軸直角方向外力を受けるボルト締結体挙動の解析的モデルの構築 : 第1報,荷重変位関係のモデル化

An Analytical model for describing the mechanical behavior of a bolted joint subjected to a transverse load has been theoretically formulated. This paper focuses on the load-displacement relation. The transverse displacement is separated into five factors: (a) bolt bending due to a transverse force acting on the thread surface, (b) bolt bending due to the thread-surface reaction moment, (c) inclination of the bolt head, (d) thread surface slip, and (e) bearing surface slip. Contact force and slip displacement are newly modeled in order to describe (d) and (e). Contact surfaces are discretized into meshes. The contact force acting on each mesh is formulated by taking into account the helical profile of the thread. The slip criterion is judged according to the Coulomb friction law. In order to maintain a mechanical equilibrium, the contact force and contact state are calculated in a self-consistent manner. As for the interaction between the thread and bearing surfaces, torque induced on the thread surface is transmitted to the bearing surface in a model of bolt torsion, relevant to the loosening rotation. The mechanism by which the reaction moment, which affects (b) to (e), is induced on the thread and bearing surfaces is also investigated. We found that the inclination of the bolt affects the reaction moment during localized thread-surface slip, while the transverse displacement of the bolt affects that during the complete thread-surface slip. The reaction moment is formulated to be proportional to the stiffness of the thread and bearing surfaces. Finally, our analytical model is applied to an M16 bolted joint and confirmed that our model agree well with the FEM result.

Analytical Modelling of the Mechanical Behavior of Bolted Joint Subjected to Transverse Loading

An analytical model for describing the mechanical behavior of a bolted joint subjected to a transverse load has been theoretically formulated. This paper focuses on the load-displacement relation. The transverse displacement is separated into five factors: (a) bolt bending due to a transverse force acting on the thread surface, (b) bolt bending due to the thread-surface reaction moment, (c) inclination of the bolt head, (d) thread surface slip, and (e) bearing surface slip. Contact force and slip displacement are newly modeled in order to describe (d) and (e). Contact surfaces are discretized into meshes. The contact force acting on each mesh is formulated by taking into account the helical profile of the thread. The slip criterion is judged according to the Coulomb friction law. In order to maintain a mechanical equilibrium, the contact force and contact state are calculated in a self-consistent manner. As for the interaction between the thread and bearing surfaces, torque induced on the thread surface is transmitted to the bearing surface in a model of bolt torsion, relevant to the loosening rotation. The mechanism by which the reaction moment, which affects (b) to (e), is induced on the thread and bearing surfaces is also investigated. We found that the inclination of the bolt affects the reaction moment during localized thread-surface slip, while the transverse displacement of the bolt affects that during the complete thread-surface slip. The reaction moment is formulated to be proportional to the stiffness of the thread and bearing surfaces. Finally, our analytical model is applied to an M16 bolted joint and confirmed that our model agree well with the FEM result.

J0403-2-3 せん断外力を受けるボルト締結体のゆるみ挙動のモデル化([J0403-2]締結・接合部の力学と評価(2):機械締結)

Mechanical behavior of a bolted joint subjected to a rotational loading and a combined loading of a rotational and a transverse load is investigated. It is confirmed that the joint behavior obtained using the proposed analytical model reproduces that obtained by FEM analysis. As to the rotational loading case, the thread surface undergoes complete slip and bolt rotates in the loosening direction in the loosening process while the bearing surface undergoes complete slip and bolt does not rotate in the tightening process. As to the combined loading case in which the joint is subjected to rotation angle of 0.12 degree and transverse displacement of 0.04 mm, the progress of loosening decreases because the bolt rotates in the tightening direction in the tightening process.

Incompressible Limits and Propagation of Acoustic Waves in Large Domains with Boundaries

We study the incompressible limit for the full Navier-Stokes-Fourier system on unbounded domains with boundaries, supplemented with the complete slip boundary condition for the velocity field. Using an abstract result of Tosio Kato we show that the energy of acoustic waves decays to zero on any compact subset of the physical space. This in turn implies strong convergence of the velocity field to its limit in the incompressible regime.

Boundary Behavior of Viscous Fluids: Influence of Wall Roughness and Friction-driven Boundary Conditions

We consider a family of solutions to the evolutionary Navier–Stokes system supplemented with the complete slip boundary conditions on domains with rough boundaries. We give a complete description of the asymptotic limit by means of Γ-convergence arguments, and identify a general class of boundary conditions.

The incompressible limit of the full Navier–Stokes–Fourier system on domains with rough boundaries

We study the incompressible limit of the full Navier–Stokes–Fourier system on condition that the boundary of the spatial domain oscillates with the amplitude and wave length proportional to the Mach number. Assuming the fluid satisfies the complete slip boundary conditions on the oscillating boundary, we identify the asymptotic limit, and, in particular, establish strong (pointwise) convergence of the velocities towards a solenoidal vector field.

Loosening-resistance evaluation of double-nut tightening method and spring washer by three-dimensional finite element analysis

The mechanisms of loosening-resistance components are investigated within the framework of the three-dimensional finite element method (FEM). In this paper, we have evaluated the ability of double-nut tightening method (DN) and spring washer (SW) to resist self-loosening due to transverse loading. We have found that if locking state is properly achieved in the tightening process, DN shows significant loosening resistance regardless of the magnitude of locking force. It was observed in this case that thread surface on the upper nut retains stuck state even if bearing-surface undergoes complete slip. However, if the locking process is not performed properly, the ability to resist loosening completely disappears. On the other hand, it is shown that SW accelerates loosening rotation of nut. The stuck area on the contact surfaces is reduced to two corner edges of the SW and the rotational force around these edges thus drastically leads to loosening before complete bearing-surface slip.

On the asymptotic limit of the Navier–Stokes system on domains with rough boundaries

We study the asymptotic behavior of solutions to the incompressible Navier–Stokes system considered on a sequence of spatial domains, whose boundaries exhibit fast oscillations with amplitude and characteristic wave length proportional to a small parameter. Imposing the complete slip boundary conditions we show that in the asymptotic limit the fluid sticks completely to the boundary provided the oscillations are non-degenerate, meaning not oriented in a single direction.

Evaluation of Loosening Resistance Performance of Conical Spring Washer by Three-dimensional Finite Element Analysis

The conical spring washer (CSW) has been considered to prevent the loosening of a bolted joint and has thus been widely employed. However, experimental results obtained in studies focusing on loosening due to transverse loading conducted by Yamamoto et al. and Sakai have shown that a CSW did not prevent loosening in any context. In the present paper, we performed three-dimensional finite element analyses of an M10 bolted joint using a CSW subjected to transverse loading and investigated its loosening resistance performance. Two kinds of axial force were applied: one was low axial force (10kN) under which a CSW is not fully compressed, and the other was high axial force (20kN) under which a CSW is fully compressed. In the case of high axial force, the CSW showed no vivid effect on preventing loosening. On the other hand, in the case of low axial force, the CSW showed two opposite effects. The negative effect was an increase in the loosening rotation angle, while the positive one was the prevention of a decrease in axial force. When complete bearing-surface slip occurs, a CSW can prevent loosening because the positive effect is larger than the negative. However, when small bearing-surface slip occurs, a CSW cannot prevent loosening because the negative effect cancels the positive one. It is supposed that the small stuck region as well as the small equivalent diameter of friction torque leads to large loosening rotation.

On the Asymptotic Limit of Flows Past a Ribbed Boundary

We consider a stationary Navier–Stokes flow in a bounded domain supplemented with the complete slip boundary conditions. Assuming the boundary of the domain is formed by a family of unidirectional asperities, whose amplitude as well as frequency is proportional to a small parameter e, we shall show that in the asymptotic limit the motion of the fluid is governed by the same system of the Navier–Stokes equations, however, the limit boundary conditions are different. Specifically, the resulting boundary conditions prevent the fluid from slipping in the direction of asperities, while the motion in the orthogonal direction is allowed without any constraint.

Small Loosening of Bolt-nut Fastener Due to Micro Bearing-Surface Slip: A Finite Element Method Study

Bolt-nut fasteners are widely used in mechanical structures due to the systems' ease of disassembly for maintenance and their relatively low cost. However, vibration-induced loosening has remained problematic. In this paper, we investigated the mechanisms of the loosening process due to micro bearing-surface slip within the framework of the three-dimensional finite element method (FEM). The results show close agreement with Kasei's experimental results. It is found that the early-stage nut rotation observed experimentally originates from simultaneous bolt-nut rotation induced by the tightening torsion of the bolt and does not correspond to loosening rotation. Therefore, loosening rotation should be defined by the relative rotation angle of the nut with respect to the bolt. It is also found that small loosening is initiated when the vibration force reaches about 50 to 60% of the critical loading necessary for bearing-surface slip. Attention should be paid to the contact state of both bearing and thread surfaces when considering the loosening of bolt-nut tightening systems. Contact states can be classified into three types: complete slip involving no sticking region, micro slip involving no constant-sticking region over a vibration cycle, and localized slip involving a constant-sticking region over a vibration cycle. It is also found that loosening rotation can proceed when either micro slip or complete slip occurs at both the thread and bearing contact surfaces.

A variational approach to moving contact line hydrodynamics

In immiscible two-phase flows, contact line denotes the intersection of the fluid-fluid interface with the solid wall. When one fluid displaces the other, the contact line moves along the wall. A classical problem in continuum hydrodynamics is the incompatibility between the moving contact line and the no-slip boundary condition, as the latter leads to a non-integrable singularity. The recently discovered generalized Navier boundary condition (GNBC) offers an alternative to the no-slip boundary condition which can resolve the moving contact line conundrum. We present a variational derivation of the GNBC through the principle of minimum energy dissipation (entropy production), as formulated by Onsager for small perturbations away from the equilibrium. Through numerical implementation of a continuum hydrodynamic model, it is demonstrated that the GNBC can quantitatively reproduce the moving contact line slip velocity profiles obtained from molecular dynamics simulations. In particular, the transition from complete slip at the moving contact line to near-zero slip far away is shown to be governed by a power-law partial slip regime, extending to mesoscopic length scales. The sharp (fluid-fluid) interface limit of the hydrodynamic model, together with some general implications of slip versus no-slip, are discussed.

The Frequency Dependence of Critical-Velocity Behavior in the Oscillatory Flow of Superfluid 4He Through a 2 × 2-μm Aperture in a Thin Foil

The critical-velocity behavior of oscillatory superfluid 4He flow through a 2 × 2-μm aperture in a 0.1-μm-thick metal foil has been studied from 0.36 to 2.10 K at frequencies from less than 50 Hz up to above 1880 Hz. The pressure remained less than 0.5 bar. In early runs during which the frequency remained below 400 Hz, the critical velocity was a nearly-linearly decreasing function of increasing temperature throughout the region of temperature studied. In runs at the lowest frequencies, isolated 2π phase slips could be observed at the onset of dissipation. In runs with frequencies higher than 400 Hz, downward curvature was observed in the decrease of critical velocity with increasing temperature. In addition, above 500 Hz an alteration in supercritical behavior was seen at the lower temperatures, involving the appearance of large-energy-loss events. These irregular events typically lasted a few tens of half-cycles of oscillation and could involve hundreds of times more energy loss than would have occurred in a single complete 2π phase slip at maximum flow. The temperatures at which this altered behavior was observed rose with frequency, from ~ 0.6 K and below at 500 Hz, to ~ 1.0 K and below at 1880 Hz.

Flow around nanospheres and nanocylinders

For micro- and nanoscale problems, boundary surface roughness often means that the usual no-slip boundary condition of fluid mechanics does not apply. Here we examine the steady low-Reynolds-number flow past a nanosphere and a circular nanocylinder in a Newtonian fluid, with the no-slip boundary condition replaced by a boundary condition which attempts to account for boundary slip due to the tangential shear at the boundary. We apply the so-called Navier boundary condition and use the method of matched asymptotic expansions. This model possesses a single parameter to account for the slip, the slip length l, which is made dimensionless with respect to the corresponding radius, which is assumed to be of the same order of magnitude as the slip length. Numerical results are presented for the two extreme cases, l = 0 corresponding to classical theory, and l → ∞ corresponding to complete slip. The streamlines for l > 0 are closer to the body than for l = 0, while the frictional drag for l > 0 is reduced below the values for l = 0, as might be expected. For the circular cylinder, results corresponding to l → ∞ are in complete accord with certain low-Reynolds-number experimental results, and this excellent agreement is much better than that predicted by the no-slip boundary condition.