Friction Distribution Research Articles

Fluid Flow Analysis for Friction Torque around Rolling Element in Ball Bearings

Ball bearings (e.g., deep-groove, angular-contact, and roller bearings) support loads in a rotor system and provide lubrication between the shaft and housing. The deep-groove ball bearings used in a turbopump do not differ significantly from angular-contact ball bearings or the bearings found in other applications. Deep-groove ball bearings consist of rolling elements, an inner raceway, an outer raceway, and a retainer to guide the rolling elements. In ball bearings, the resistive (churning or drag) forces and torques acting on the rolling elements and raceways are affected by the fluid flow rate and direction, as well as the rotational speed. These churning and drag forces and torques affect the internal dissipation or power losses into the bearing, which become very significant for high-speed applications. This study numerically investigated the characteristics of the flow conditions for deep-groove ball bearings, with a particular focus on the friction distribution on the rolling elements. A simple analytical model of the fluid flow inside a ball bearing was developed using a computational analysis, and the flow characteristics at high rotational speeds are presented.

Effects of fault heterogeneity on seismic energy and spectrum

We study the effects of friction heterogeneity on the dynamics of a seismogenic fault. To this aim, we consider a fault model containing two asperities with different static frictions and a rate-dependent dynamic friction. We consider the seismic events produced by the consecutive failure of the two asperities and study their properties as functions of the ratio between static frictions. In particular, we calculate the moment rate, the stress evolution during fault slip, the average stress drop, the partitioning of energy release, the seismic energy, the far-field waveforms and the spectrum of seismic waves. These quantities depend to various extent on the friction distribution on the fault. In particular, the stress distribution on the fault is always strongly heterogeneous at the beginning of the seismic event. Seismic energy and frictional heat decrease with increasing friction heterogeneity, while seismic efficiency is constant. We obtain an equation relating seismic efficiency to the parameters of the friction law, showing that the efficiency is maximum for smaller values of dynamic friction. The seismic spectrum depends on the friction distribution as to the positions and the values of the minima. However, under the model assumption that the slip durations are the same for both asperities, the corner frequency is independent of the friction distribution, but it depends on the friction law and on the coupling between asperities. The model provides a relation between the total radiated energy and the seismic moment that is consistent with the empirical relation between the two quantities. The fault model with one asperity is also considered as a particular case. The model is applied to the 1965 Rat Islands (Alaska) earthquake and shows the role of fault heterogeneity in controlling the spatial distribution of stress drop as well as the time dependence and the final amount of radiated energy.

Numerical investigation on scaling a pure friction isolation system for civil structures in shaking table model tests

Many Coulomb friction-based devices have been used for seismic isolation of modern civil structures. Aiming at a practical problem that if the friction action could be scaled in a shaking table model test, a base isolation system using Coulomb friction was numerically scaled in different ways by considering the gravity distortion, friction distribution and other influence factors. The seismic responses back calculated from the scaled models were compared with those of the full-scale model to evaluate the accuracy of scale theory for such a Coulomb friction action. The above numerical results show that the scale theory is still applicable for the uniform and non-uniform friction distribution patterns with nonlinear characteristics. The gravity distortion and uneven friction distribution are the most important factors, causing the errors of scale theory for the Coulomb friction system. However, the unallowable errors, caused by the un-scaled gravity acceleration on common shaking tables, can be avoided by reasonably changing the friction coefficients at the scaled friction interface. And other unallowable errors, caused by the uneven friction distribution, can be prevented if the specific positions with different friction coefficients for the full-scale model are proportionally moved with the scaled contact surface.

Regional modeling of the Shirase drainage basin, East Antarctica: full Stokes vs. shallow ice dynamics

Abstract. A hierarchy of approximations of the force balance for the flow of grounded ice exists, ranging from the most sophisticated full Stokes (FS) formulation to the most simplified shallow ice approximation (SIA). Both are implemented in the ice flow model Elmer/Ice, and we compare them by applying the model to the East Antarctic Shirase drainage basin. First, we apply the control inverse method to infer the distribution of basal friction with FS. We then compare FS and SIA by simulating the flow of the drainage basin under present-day conditions and for three scenarios 100 years into the future defined by the SeaRISE (Sea-level Response to Ice Sheet Evolution) project. FS reproduces the observed flow pattern of the drainage basin well, in particular the zone of fast flow near the grounding line, while SIA generally overpredicts the surface velocities. As for the transient scenarios, the ice volume change (relative to the constant-climate control run) of the surface climate experiment is nearly the same for FS and SIA, while for the basal sliding experiment (halved basal friction), the ice volume change is ∼ 30 % larger for SIA than for FS. This confirms findings of earlier studies that, in order to model ice sheet areas containing ice streams and outlet glaciers with high resolution and precision, careful consideration must be given to the choice of a suitable force balance.

Modeling and experimental identification of contact pressure and friction for the analysis of non-conforming elastic contact

In this paper, we propose an experiment-based method for the modeling and the identification of the contact pressure and friction distribution on the interface of a non-conforming contact. In this method a two-dimensional contact model is established. The distributed contact pressure and friction are approximated by Taylor series and their relationship with the local displacements near the contact interface are modeled by using a half-space based approach. The parameters of the proposed contact model include the contact center, the half length of the interface, and the orders and coefficients of the Taylor series. They are identified by minimizing the residual between the computed displacement field and the measured one through an alternating optimization. The contact pressure and friction are reconstructed by the optimal parameters. A full-field optical method, namely segmentation-aided digital image correlation, is used not only to experimentally measure the local displacements but also to initialize the model parameters. The proposed mechanical modeling requires fewer assumptions compared with the classic models. The parameter identification only uses the local displacements and does not require boundary conditions of the contact members. The results of the simulated and real-world experiments show that the proposed method is able to reliably recover the contact stress and it is robust against the displacement measurement uncertainty.

Bond graph-based dynamic model of planetary roller screw mechanism with consideration of axial clearance and friction

To reveal the dynamic characteristics of planetary roller screw mechanism, a dynamic model of planetary roller screw mechanism is developed in this study, which is based on the bond graph theory that accounts for friction, axial clearance, and screw stiffness. First, the bond graph models of friction, axial clearance, and load distribution are presented. Then, a bond graph model of the entire planetary roller screw mechanism for the dynamic analysis is established using the 20-sim software package, and the dynamic equations are solved using the Runge–Kutta–Fehlberg algorithm. Finally, the axial speed, axial acceleration, and contact force of the components are derived under different axial loads and with different axial clearances. Furthermore, the dynamic friction characteristics at different angular velocities of the screw and the dynamic stiffnesses for different axial clearances are also obtained. The results can provide a theoretical basis for planetary roller screw mechanism design with consideration of dynamic characteristics.

The coupled effect of bearing misalignment and friction on vibration characteristics of a propulsion shafting system

The propulsion shafting system of ships is usually supported, in part, by water-lubricated rubber bearings, which often work at mixed or boundary lubrication state under heavy-load and low-speed conditions, resulting in strong friction on the bearing–shaft interface and even abnormal vibration in the overall system. In addition, bearing misalignment can further affect the distribution of friction and consequently change the lateral and torsional vibration characteristics of the shafting system. In this work, the rubber bearing was simplified into parallel-distributed springs and the water film was neglected. The dynamic model of the propulsion shafting system was built with the finite element method and reduced by mode truncation. The coupled effect of bearing misalignment and friction was subsequently analyzed with this reduced model and the fourth-order Runge–Kutta method. Finally, lateral and torsional vibration characteristics of the overall system under different bearing misalignment were obtained, which can be used in the identification or diagnosis of abnormal vibration induced by friction.

Connecting depth limits of interseismic locking, microseismicity, and large earthquakes in models of long‐term fault slip

AbstractThickness of the seismogenic zone is commonly determined based on the depth of microseismicity or the fault locking depth inferred from geodetic observations. The relation between the two estimates and their connection to the depth limit of large earthquakes remain elusive. Here we explore the seismic and geodetic observables in models of faults governed by laboratory‐based friction laws that combine quasi‐static rate‐and‐state friction and enhanced dynamic weakening. Our models suggest that the transition between the locked and fully creeping regions can occur over a broad depth range. The effective locking depth, Delock, associated with concentrated loading and promoting microseismicity, is located at the top of this transition zone; the geodetic locking depth, Dglock, inverted from surface geodetic observations, corresponds to the depth of fault creeping with approximately half of the long‐term rate. Following large earthquakes, Delock either stays unchanged or becomes shallower due to creep penetrating into the shallower locked areas, whereas Dglock deepens as the slip deficit region expands, compensating for the afterslip. As the result, the two locking depths diverge in the late interseismic period, consistent with available seismic and geodetic observations from several major fault segments in Southern California. We find that Dglock provides a bound on the depth limit of large earthquakes in our models. However, the assumed layered distribution of fault friction and simple depth estimates are insufficient to characterize more heterogeneous faults, e.g., ones with significant along‐strike variations. Improved observations and models are needed to illuminate physical properties and seismic potential of fault zones.

Recovery of a supersonic turbulent boundary layer after an expansion corner

Supersonic turbulent flows at Mach 2.7 over expansion corners with deflection angles of 0° (flat plate), 2°, and 4° have been studied using direct numerical simulation. Distributions of skin friction, pressure, velocity, and boundary layer growth show that the turbulent boundary layer experiences a recovery from a non-equilibrium to an equilibrium state downstream of the expansion corner. Analysis of velocity profiles indicates that the streamwise velocity undergoes a reduction in the near-wall region even though the velocity in the core part of the boundary layer is accelerated after the expansion corner. Growth of the boundary layer was evaluated and a higher shape factor was found in the expansion cases. Turbulence was found to be mostly suppressed downstream of the corner, and throughout the recovery region, even though turbulence is regenerated in the near-wall region. The expansion ramp increases the near-wall streak spacing compared to a flat plate, and turbulent kinetic energy profiles and budgets exhibit a characteristic two-layer structure. Near-wall turbulence recovers to a balance between the local production and dissipation equilibrium more quickly in the inner layer than in the outer layer. The two-layer structure is due to a history effect of turbulence decay in the outer part of the boundary layer downstream of the expansion corner, with limited momentum and energy exchange between the inner layer and the main stream.

Redifferentiated Chondrocytes for the Repair of Articular Cartilage Lesions

Objectives:Biological therapies such as autologous chondrocyte implantation which use serially passaged chondrocytes to repair cartilage defects, are often unsuccessful as they lead to the formation of fibrocartilage. Fibrocartilage is rich in collagen type 1 (Col1) and lacks the structural complexity, low friction, and load distribution properties of articular cartilage. Fibrocartilage forms as a result of the phenotype of passaged chondrocytes. When serially passaged in monolayer to increase cell numbers, chondrocytes lose their phenotype in a process termed “dedifferentiation”. This is characterized by a loss in the production of collagen type II (Col2) and aggrecan (Acan), the major extracellular matrix molecules of articular cartilage, and an increase in the production of Col1. Therefore, to increase the success of therapies which use passaged chondrocytes, these cells must be redifferentiated to re-establish an articular cartilage phenotype prior to implantation in a cartilage lesion. Transforming growth factor beta (TGFβ) signalling is known to play important roles in both cell differentiation and articular cartilage repair. However, intra-articular injections with TGFβ have been shown to result in osteophyte formation and fibrosis of synovial tissues. Therefore, redifferentiating passaged chondrocytes in vitro using TGFβ prior to their use in vivo may be a better alternative. Fibrin glue is commonly used in orthopaedics to maintain cells in a cartilage lesion, however the effects of fibrin glue on chondrocytes have not been fully investigated. Thus we hypothesize that passaged chondrocytes redifferentiated in vitro with TGFβ will maintain their phenotype and form articular cartilage-like tissue when embedded in fibrin glue in the absence of further exogenous supplementation with TGFβ in vitro.Methods:Chondrocytes were enzymatically isolated from rabbit articular cartilage and serially passaged in monolayer twice (P2) to increase cell number and facilitate dedifferentiation. P2 cells were cultured in scaffold-free 3D using a chondrogenic serum-free media supplemented with 10ng/ml TGFβ3 to facilitate redifferentiation. Redifferentiated chondrocytes were then embedded in fibrin glue (Tisseel, Baxter) at 1.5 x 106 cells/20uL and cultured for 2 weeks in vitro in the absence of TGFβ3. Controls were P2 cells that were not redifferentiated with TGFB3 prior to embedding in fibrin glue. Histology and immunohistochemistry were used to assess tissue formation and cell phenotype.Results:Redifferentiated chondrocytes accumulated more matrix rich in Col2 and Acan than controls (Figure 1). Furthermore, redifferentiated chondrocytes had a round cell shape characteristic of articular chondrocytes. The use of fibrin glue did not impair the ability of redifferentiated chondrocytes to accumulate matrix nor did it affect cell phenotype.Conclusion:Redifferentiated chondrocytes in fibrin glue may be a better alternative to passaged chondrocytes for cell based articular cartilage repair therapies as they accumulate more Col2 and Acan containing matrix than undifferentiated P2. In vivo studies are required to elucidate the potential for redifferentiated chondrocytes in cartilage repair.

Relationship between the real contact area and contact force in pre-sliding regime**Project supported by the National Natural Science Foundation of China (Grant No. 11272171), the Natural Science Foundation of Beijing City, China (Contract No. 3172017), and the Education Ministry Doctoral Fund of China (Grant No. 20120002110070).

The pre-sliding regime is typically neglected in the dynamic modelling of mechanical systems. However, the change in contact state caused by static friction may decrease positional accuracy and control precision. To investigate the relationship between contact status and contact force in pre-sliding friction, an optical experimental method is presented in this paper. With this method, the real contact state at the interface of a transparent material can be observed based on the total reflection principle of light by using an image processing technique. A novel setup, which includes a pair of rectangular trapezoidal blocks, is proposed to solve the challenging issue of accurately applying different tangential and normal forces to the contact interface. The improved Otsu’s method is used for measurement. Through an experimental study performed on polymethyl methacrylate (PMMA), the quantity of contact asperities is proven to be the dominant factor that affects the real contact area. The relationship between the real contact area and the contact force in the pre-sliding regime is studied, and the distribution of static friction at the contact interface is qualitatively discussed. New phenomena in which the real contact area expands along with increasing static friction are identified. The aforementioned relationship is approximately linear at the contact interface under a constant normal pressure, and the distribution of friction stress decreases from the leading edge to the trailing edge.

Magneto-nanofluid flow with heat transfer past a stretching surface for the new heat flux model using numerical approach

PurposeSheet processing of magnetic nanomaterials is emerging as a new branch of smart materials’ manufacturing. The efficient production of such materials combines many physical phenomena including magnetohydrodynamics (MHD), nanoscale, thermal and mass diffusion effects. To improve the understanding of complex inter-disciplinary transport phenomena in such systems, mathematical models provide a robust approach. Motivated by this, this study aims to develop a mathematical model for steady, laminar, MHD, incompressible nanofluid flow, heat and mass transfer from a stretching sheet.Design/methodology/approachThis study developed a mathematical model for steady, laminar, MHD, incompressible nanofluid flow, heat and mass transfer from a stretching sheet. A uniform constant-strength magnetic field is applied transversely to the stretching flow plane. The Buongiorno nanofluid model is used to represent thermophoretic and Brownian motion effects. A non-Fourier (Cattaneo–Christov) model is used to simulate thermal conduction effects, of which the Fourier model is a special case when thermal relaxation effects are neglected.FindingsThe governing conservation equations are rendered dimensionless with suitable scaling transformations. The emerging nonlinear boundary value problem is solved with a fourth-order Runge–Kutta algorithm and also shooting quadrature. Validation is achieved with earlier non-magnetic and forced convection flow studies. The influence of key thermophysical parameters, e.g. Hartmann magnetic number, thermal Grashof number, thermal relaxation time parameter, Schmidt number, thermophoresis parameter, Prandtl number and Brownian motion number on velocity, skin friction, temperature, Nusselt number, Sherwood number and nanoparticle concentration distributions, is investigated.Originality/valueA strong elevation in temperature accompanies an increase in Brownian motion parameter, whereas increasing magnetic parameter is found to reduce heat transfer rate at the wall (Nusselt number). Nanoparticle volume fraction is observed to be strongly suppressed with greater thermal Grashof number, Schmidt number and thermophoresis parameter, whereas it is elevated significantly with greater Brownian motion parameter. Higher temperatures are achieved with greater thermal relaxation time values, i.e. the non-Fourier model predicts greater values for temperature than the classical Fourier model.

Creep stability of the proposed AIDA mission target 65803 Didymos: I. Discrete cohesionless granular physics model

As the target of the proposed Asteroid Impact & Deflection Assessment (AIDA) mission, the near-Earth binary asteroid 65803 Didymos represents a special class of binary asteroids, those whose primaries are at risk of rotational disruption. To gain a better understanding of these binary systems and to support the AIDA mission, this paper investigates the creep stability of the Didymos primary by representing it as a cohesionless self-gravitating granular aggregate subject to rotational acceleration. To achieve this goal, a soft-sphere discrete element model (SSDEM) capable of simulating granular systems in quasi-static states is implemented and a quasi-static spin-up procedure is carried out. We devise three critical spin limits for the simulated aggregates to indicate their critical states triggered by reshaping and surface shedding, internal structural deformation, and shear failure, respectively. The failure condition and mode, and shear strength of an aggregate can all be inferred from the three critical spin limits. The effects of arrangement and size distribution of constituent particles, bulk density, spin-up path, and interparticle friction are numerically explored. The results show that the shear strength of a spinning self-gravitating aggregate depends strongly on both its internal configuration and material parameters, while its failure mode and mechanism are mainly affected by its internal configuration. Additionally, this study provides some constraints on the possible physical properties of the Didymos primary based on observational data and proposes a plausible formation mechanism for this binary system. With a bulk density consistent with observational uncertainty and close to the maximum density allowed for the asteroid, the Didymos primary in certain configurations can remain geo-statically stable without requiring cohesion.

Analysis of uplift bearing capacity of expanded pile

The research on the uplift bearing capacity of expanded pile is less, which lead to develop slowly of mechanism of expanded pile. The finite element software is used to simulate the bearing capacity of expanded pile, and the friction between the pile and soil is simulated by surface contact. The simulations show the ultimate bearing capacity and the distribution of side friction of the expanded pile. Along with the displacement moves bigger, the side friction of upper expanded pile is fully used. When the displacement moves to a special level, the side friction of whole pile is fully used. If the load is bigger than the 25000kPa, the expanded pile will be destroyed.

Drag and inertia coefficients for a circular cylinder in steady plus low-amplitude oscillatory flows

Computer simulations of steady plus low-amplitude oscillatory flow about a circular cylinder are reported at a fixed Reynolds number of 150 based on the steady component. The conventional Keleugan–Carpenter number based on the oscillatory component is fixed at π/5. The oscillation frequency is varied so as to study a wide spectrum of flows where inertial forces dominate at one end and viscous drag forces at the other as a function of the modified Keleugan–Carpenter number. The hydrodynamic force on the cylinder in-line with the flow direction is represented by Morison's equation and an extended version with three terms. The drag and inertia coefficients in Morison's equation are determined by least-squares fits to data directly computed from integration of skin friction and pressure distributions around the periphery of the cylinder. The root-mean-square value of the residue of reconstructed minus directly-computed forces varies between 2 and 41% depending on the flow parameters. Comparable results can be obtained with a semi-theoretical approach using inviscid inertia and quasi-steady viscous drag terms. Physical explanations for the variation of the force coefficients are provided and implications for pertinent flow–structure interactions are discussed.

Modeling of steady Herschel–Bulkley fluid flow over a sphere

Characteristics of the incompressible flow of Herschel–Bulkley fluid over a sphere were studied via systematic numerical modeling. A steady isothermal laminar flow mode was considered within a wide range of flow parameters: the Reynolds number 0 < Re ≤ 200, the Bingham number 0 ≤ Bn ≤ 100, and the power index 0.3 ≤ n ≤ 1. The numerical solution to the hydrodynamic equations was obtained using the finite volume method in the axisymmetric case. The changes in flow structures, pressure and viscous friction distribution, and integral drag as a function of the flow rate and fluid rheology are shown. Depending on whether plastic or inertial effects dominate in the flow, the limiting cases were identified. The power law and Bingham fluid flows were studied in detail as particular cases of the Herschel–Bulkley rheological model. Based on the modeling results, a new correlation was developed that approximates the calculated data with an accuracy of about 5% across the entire range of the input parameters. This correlation is also applicable in the particular cases of the power law and Bingham fluids.

Hybrid oil film approach to measuring skin friction distribution

This paper describes a technique for quantitatively measuring the time-averaged skin friction distribution on a wind tunnel test model. The technique is a hybrid oil film approach that is based on the combination of the qualitative skin friction distribution obtained from luminescent oil film and the quantitative local skin friction measurements obtained from oil film interferometry in another blowing of the same flow condition. To demonstrate its validity, the proposed method was applied to the flow field around a vortex generator on a flat plate, and successfully measured the quantitative skin friction distribution.

Mitigation of shock-induced flow separation using magnetohydrodynamic flow control

A numerical investigation is carried out to demonstrate a proof of concept, magnetohydrodynamics-based active flow control, for mitigation of laminar flow separation over a flat plate due to shock wave–boundary layer interaction. The CERANS-MHD code has been used to solve the governing resistive magnetohydrodynamic equations discretized in finite-volume framework. The AUSM-PW+ flux function is used in modelling the advection terms and central differencing is used in modelling the resistive terms. Powell’s source term method is used for divergence cleaning of the magnetic field. The Hartmann number is varied from 0 to 12,000 to effectuate mitigation of flow separation, with the magnetic field applied at the wall and oriented transverse to the flat plate flow direction. Due to the Hartmann effect, flow separation is observed to be suppressed with increase in Hartmann number beyond 6000. However, the overall magnitude of skin friction distribution increases drastically, resulting in large increase in skin friction drag as compared with the non-magnetic case, and is a cause of concern.

Kinetic simulation of a supersonic compressible flow over different geometry bodies

Numerical simulation of a supersonic compressible gas flow over different geometry bodies, namely, a flat plate, a hollow cylinder flare and a backward-facing step for different Reynolds numbers based on the numerical solution of the S-model of the Boltzmann equation is presented. Computations are performed for different thermal boundary conditions: constant wall temperature and adiabatic wall. The flow structure and distributions of surface pressure, skin friction and heat transfer coefficients are studied. Comparison with available analytical, Direct Simulation Monte Carlo method results and experimental data is carried out and demonstrated good agreement. The appearance of separation region caused by an interaction of boundary layer with a shock wave induced by a compression corner for both flare and backward-facing step geometries is observed.

Comparison of Cohesion (c’), and Angle of Internal Friction (Ф’) Distribution in Highland Area of Kundasang by using Ordinary Kriging and Simple Kriging.

The objective of the research is to determine the distribution of cohesion (c’), and angle of internal friction (?’) values for the highland area of Kundasang, Sabah by using kriging. A set of data from two adjacent site in Kundasang were collected from the site investigation report. There are three main stages in determining these parameters. The first stage is to use ordinary kriging methods to determine the modelling for these parameters. The second stage is to compare the results from ordinary kriging methods to simple kriging methods. The third stage is to produce the mapping for these parameters in the site, which could be used for slope stability and foundation design.