圆柱体的滚动摩擦系数的测量研究

从圆柱体在斜面上的基本受力分析入手,推导圆柱体沿斜面运动过程中的发生滚动的临界角及滚动摩擦系数的关系式。并通过简单的实验装置测定了铁质圆柱体与玻璃的滚动摩擦系数和静摩擦系数分别约为0.0921和0.121。理论与实验结果基本符合,表明该实验方法对于测定静摩擦系数和滚动摩擦系数的有效性,也为力学基本问题的研究提供了方法。     

Rubber friction on smooth surfaces

We study the sliding friction for viscoelastic solids, e.g., rubber, on hard flat substrate surfaces. We consider first the fluctuating shear stress inside a viscoelastic solid which results from the thermal motion of the atoms or molecules in the solid. At the nanoscale the thermal fluctuations are very strong and give rise to stress fluctuations in the MPa-range, which is similar to the depinning stresses which typically occur at solid-rubber interfaces, indicating the crucial importance of thermal fluctuations for rubber friction on smooth surfaces. We develop a detailed model which takes into account the influence of thermal fluctuations on the depinning of small contact patches (stress domains) at the rubber-substrate interface. The theory predicts that the velocity dependence of the macroscopic shear stress has a bell-shaped form, and that the low-velocity side exhibits the same temperature dependence as the bulk viscoelastic modulus, in qualitative agreement with experimental data. Finally, we discuss the influence of small-amplitude substrate roughness on rubber sliding friction.     

Contact mechanics and rubber friction for randomly rough surfaces with anisotropic statistical properties

In this paper we extend the theory of contact mechanics and rubber friction developed by one of us (B.N.J. Persson, J. Chem. Phys. 115, 3840 (2001)) to the case of surfaces with anisotropic surface roughness. As an application we calculate the viscoelastic contribution to the rubber friction. We show that the friction coefficient may depend significantly on the sliding direction, while the area of contact depends weakly on the sliding direction. We have carried out experiments for rubber blocks sliding on unidirectionally polished steel surfaces. The experimental data are in a good qualitative agreement with the theory.     

Rivulet flow on the outer surface of an inclined cylinder

A study of the three-dimensional flow of a liquid film (rivulet) over the external part of an inclined cylinder was conducted for liquids with various physical properties. Patterns of the flow regimes were constructed. Good agreement is observed between the experimental data on the thickness and wall friction with the calculation with an asymptotic model in the case of a waveless rivulet. A comparison of the evolution of natural waves on rivulets with the theory of waves of maximal growth shows good agreement for small Re numbers. During the experiments, the wave characteristics of excited waves on a rivulet were investigated. The thickness, amplitude, frequency, and phase velocity of the waves over a wide range of variable parameters are given. Phase velocity integrated functions of the amplitude are constructed for various liquids. The friction on the cylinder wall is measured in the presence of natural and excited waves. The effects of wave regimes on the average values and RMS (root-mean-square) friction pulsations are studied.     

Debonding dynamics of pressure-sensitive adhesives: 3D block model

We develop a 3-dimensional mechanical model which describes cavity expansions in a viscoelastic solid medium during the debonding phase of the probe-tack test. The stress-strain curves are in good agreement with experiments for the typical pressure-sensitive adhesives. We also show that the separation speed dependence can be explained by viscous dissipations due to large strain rates around the cavities.     

Pattern formation during deformation of a confined viscoelastic layer: from a viscous liquid to a soft elastic solid

We study pattern formation during tensile deformation of confined viscoelastic layers. The use of a model system [poly(dimethylsiloxane) with different degrees of cross-linking] allows us to go continuously from a viscous liquid to an elastic solid. We observe two distinct regimes of fingering instabilities: a regime called "elastic" with interfacial crack propagation, where the fingering wavelength scales only with the film thickness, and a bulk regime called "viscoelastic," where the fingering instability shows a Saffman-Taylor-like behavior. We find good quantitative agreement with theory in both cases and present a reduced parameter describing the transition between the two regimes and allowing us to predict the observed patterns over the whole range of viscoelastic properties.     

The influence of heat radiation on mixed convection boundary layer flow of a viscoelastic fluid over a circular cylinder with constant surface temperature

The influence of mixed convection boundary layer flow of a viscoelastic fluid over an isothermal horizontal circular cylinder has been analyzed. The boundary layer equations governing the problem are reduced to dimensionless nonlinear partial differential equations and then solved numerically using Keller-box method. Skin friction coefficient and Nusselt number are emphasized specifically. These quantities are displayed against curvature parameter. Effects of mixed convection parameter and radiation-conduction parameter on skin friction coefficient and Nusselt number are illustrated through graphs and table. The boundary layer separation points along the surface of cylinder are also calculated with/without radiation, and a comparison is shown. The presence of radiation helps to reduce the skin friction coefficient in opposing flow case and enhances it for assisting flow case. The increase in value of radiation-conduction parameter helps increase the value of skin friction coefficient and Nusselt number for viscoelastic fluids. The boundary layer separation delays due to thermal radiation.     

Finite element method for viscoelastic medium with damage and the application to structural analysis of solid rocket motor grain

This paper studies the damage-viscoelastic behavior of composite solid propellants of solid rocket motors(SRM).Based on viscoelastic theories and strain equivalent hypothesis in damage mechanics,a three-dimensional(3-D)nonlinear viscoelastic constitutive model incorporating with damage is developed.The resulting viscoelastic constitutive equations are numerically discretized by integration algorithm,and a stress-updating method is presented by solving nonlinear equations according to the Newton-Raphson method.A material subroutine of stress-updating is made up and embedded into commercial code of Abaqus.The material subroutine is validated through typical examples.Our results indicate that the finite element results are in good agreement with the analytical ones and have high accuracy,and the suggested method and designed subroutine are efficient and can be further applied to damage-coupling structural analysis of practical SRM grain.     

Geometry independence of the normalized relaxation functions of viscoelastic materials in indentation

The normalized relaxation modulus represents a salient feature of viscoelastic materials and its determination is of great significance for various applications. From the normalized relaxation modulus, for instance, one can derive the loss factor of a viscoelastic polymer and judge whether a material is suitable for damping applications or not. By using dimensional analysis and the elastic–viscoelastic correspondence principle, the normalized relaxation function of a linear viscoelastic material obtained from indentation relaxation tests is shown to depend only on the indentation load but not on the indenter geometry and the shape of the indented solid. The result could enable circumvention of the difficulties encountered in the calibration of the indenter geometry and the preparation of indented samples. Numerical simulations are performed on a number of cases of practical interest, including the spherical indentation test of a soft layer lying on a rigid substrate, a flat punch indenter indenting into a soft layer with a rough surface bonded to a rigid substrate, a rigid indenter with irregular shape indenting into a particle, inclined contact of a cylindrical indenter with a cylinder, and indentation of porous substrates. The numerical examples demonstrate that the conclusion from the theoretical analysis is valid for all these situations.     

Capillarity driven instability of a soft solid

We report the observation of a Plateau instability in a thin filament of solid gel with a very small elastic modulus. A longitudinal undulation of the surface of the cylinder reduces its area thereby triggering capillary instability, but is counterbalanced by elastic forces following the deformation. This competition leads to a nontrivial instability threshold for a solid cylinder. The ratio of surface tension to elastic modulus defines a characteristic length scale. The onset of linear instability is when the radius of the cylinder is one-sixth of this length scale, in agreement with theory presented here.     

Rigidity percolation in particle-laden foams

We study the viscoelastic behavior of aqueous foam mixed with solid noncolloidal particles. We show that adding a tiny amount of grains can enhance the elastic and loss shear moduli by more than 1 order of magnitude. The scaling of these moduli with solid volume fraction is in qualitative agreement with that predicted by an effective-medium rigidity percolation model. We present a simple model, based on capillary attraction, to explain the particle-size dependence of the threshold.     

Dynamic simulation of multi-component viscoelastic fluids using the lattice Boltzmann method

We develop a discrete model for multi-component viscoelastic fluids based on the lattice Boltzmann method. The model newly introduces the kinetics of polymers so that viscoelasticity is included. We perform three-dimensional simulations of a Newtonian drop in shear flow of a viscoelastic fluid in order to investigate the validity of the current model. In the investigation, effects of viscoelasticity on deformation and orientation of drops are evaluated. The simulation results are compared with experimental measurements quantitatively, and they show good agreement with each other.     

Polymer cover induced self-excited vibrations of nipped rolls

As a result of increased speeds, the dynamic instability of rotatory machines including polymer-covered nipped rolls has grown. The instability originates from the viscoelastic behavior of the covers and leads to strong barring vibrations, which limit the operating speed of many machines. In this work, the self-excited vibrations of a nipped two-roll system with a polymer cover on the other roll are investigated using an analytical model developed for the roll system. The viscoelastic properties of the cover are accounted for by the standard linear solid (SLS) model. The numerical results display wave-like roll cover deformation patterns, separate instability regions of the system and moving wave patterns near the resonances. The roll system is unstable when the excitation frequency of the polygonal cover deformation lies in the vicinity of the higher eigenfrequency of the system. By using a speed-up ramp, it is shown that at high speeds the instability regions may become too wide and unstable to be crossed in industrial machines. An experiment was carried out, and a good agreement is found between the numerical and experimental results.     

Numerical solution of an extended White–Metzner model for eccentric Taylor–Couette flow

In this study, we have developed a new numerical approach to solve differential-type viscoelastic fluid models for a commonly used benchmark problem, namely, the steady Taylor—Couette flow between eccentric cylinders. The proposed numerical approach is special in that the nonlinear system of discretized algebraic flow equations is solved iteratively using a Newton–Krylov method along with an inverse-based incomplete lower-upper preconditioner. The numerical approach has been validated by solving the benchmark problem for the upper-convected Maxwell model at a large Deborah number. Excellent agreement with the numerical data reported in the literature has been found. In addition, a parameter study was performed for an extended White–Metzner model. A large eccentricity ratio was chosen for the cylinder system in order to allow flow recirculation to occur. We detected several interesting phenomena caused by the large eccentricity ratio of the cylinder system and by the viscoelastic nature of the fluid. Encouraged by the results of this study, we intend to investigate other polymeric fluids having a more complex microstructure in an eccentric annular flow field.     

Frictional coupling between sliding and spinning motion

The tangential motion at the contact of two solid objects is studied. It consists of a sliding and a spinning degree of freedom (no rolling). We show that the friction force and torque are inherently coupled. As a simple test system, a sliding and spinning disk on a horizontal flat surface is considered. We calculate, and also measure, how the disk slows down and find that it always stops its sliding and spinning motion at the same moment. We discuss the impact of this coupling between friction force and torque on the physics of granular materials.     

Theoretical development of a simplified wheelset model to evaluate collision-induced derailments of rolling stock

A theoretical method is proposed to predict and evaluate collision-induced derailments of rolling stock by using a simplified wheelset model and is verified with dynamic simulations. Because the impact forces occurring during collision are transmitted from the car body to the bogies and axles through suspensions, rolling stock leads to derailment as a result of the combination of horizontal and vertical impact forces applied to the axle and a simplified wheelset model enforced at the axle can be used to theoretically formulate derailment behaviors. The derailment type depends on the combination of the horizontal and vertical forces, the flange angle and the friction coefficient. According to collision conditions, wheel-climb, wheel-lift or roll-over derailment can occur between the wheel and the rail. In this theoretical derailment model of a simplified wheelset, the derailment types are classified as Slip-up, Slip/roll-over, Climb-up, Climb/roll-over and pure Roll-over according to the derailment mechanisms between the wheel and the rail and the theoretical conditions needed to generate each derailment mechanism are proposed. The theoretical wheelset model is verified by dynamic simulation and its applicability is demonstrated by comparing the simulation results of the theoretical wheelset model with those of an actual wheelset model. The theoretical derailment wheelset model is in good agreement with the virtual testing model simulation for a collision-induced derailment of rolling stock.     

Stochastic rolling of a rigid sphere in weak adhesive contact with a soft substrate

We study the rolling motion of a small solid sphere on a fibrillated rubber substrate in an external field in the presence of a Gaussian noise. From the nature of the drift and the evolution of the displacement fluctuation of the ball, it is evident that the rolling is controlled by a complex non-linear friction at a low velocity and a low noise strength (K), but by a linear kinematic friction at a high velocity and a high noise strength. This transition from a non-linear to a linear friction control of motion can be discerned from another experiment in which the ball is subjected to a periodic asymmetric vibration in conjunction with a random noise. Here, as opposed to that of a fixed external force, the rolling velocity decreases with the strength of the noise suggesting a progressive fluidization of the interface. A state (K) and rate (V) dependent friction model is able to explain both the evolution of the displacement fluctuation as well as the sigmoidal variation of the drift velocity with K. This research sets the stage for studying friction in a new way, in which it is submitted to a noise and then its dynamic response is studied using the tools of statistical mechanics. Although more works would be needed for a fuller realization of the above-stated goal, this approach has the potential to complement direct measurements of friction over several decades of velocities and other state variables. It is striking that the non-Gaussian displacement statistics as observed with the stochastic rolling is similar to that of a colloidal particle undergoing Brownian motion in contact with a soft microtubule.     

Transverse shear oscillator investigation of boundary lubrication in weakly adhered films

We investigate the boundary lubrication in weakly adhered molecularly thin films deposited between a sphere and a plane, below the sliding threshold. The shear contact stiffness and interfacial dissipation at the micrometer scale are determined with a high-frequency quartz oscillator. Two distinct behaviors are found as a function of the shear oscillation: a linear viscoelastic response at low amplitude and a nonlinear frictional microslip at high amplitude. A friction model is proposed to analyze the data, which allows evaluating the shear strength, the friction coefficient, and the interfacial viscosity at different solid interfaces under low load.     

Ultrasonic pulse waves in cancellous bone analyzed by finite-difference time-domain methods

The trabecular frame of cancellous bone has a high degree of porosity, anisotropy and inhomogeneity. The propagation of ultrasonic waves in cancellous bone is significantly affected by the trabecular structure. In this paper, two two-dimensional finite-difference time-domain (FDTD) methods, which were the popular viscoelastic FDTD method for a viscoelastic medium and Biot's FDTD method for a fluid-saturated porous medium, have been applied to numerically analyze the ultrasonic pulse waves propagating through bovine cancellous bone in the directions parallel and perpendicular to the trabecular alignment. The Biot's fast and slow longitudinal waves, which were identified in previous experiments for the propagation parallel to the trabecular orientation, could be analyzed using Biot's FDTD method rather than the viscoelastic FDTD method. For the single wave propagation in the perpendicular direction, on the other hand, the viscoelastic FDTD result was found to be in more good agreement with the experimental result.     

Viscoelasticity of dynamically self-assembled paramagnetic colloidal clusters

Paramagnetic particles in a liquid above a solid dynamically self-assemble into two-dimensional (2D) viscoelastic clusters in a processing magnetic field if the precession angle exceeds the magic angle. Hexagonal clusters rotate with a frequency proportional to the precession frequency of the magnetic field. The rotation is explained by viscoelastic shear waves excited in the clusters that can be visualized slightly above the magic angle. The cluster rotation and the visualization of viscoelastic modes are independent techniques to probe the rheological properties of the cluster. We find agreement between both techniques when determining the 2D cluster viscosity eta(c) approximately 10(-11) N s/m.