A control volume-based discretization of the Reynolds equation for the numerical solution of elastohydrodynamic lubrication problems

This paper deals with the discretization of the one-dimensional Reynolds equation coupled with the film shape equation, that is used for the numerical solution of elastohydrodynamically lubricated contacts. The derivation of the developed discretization formula is based on the control volume approach. To reduce the discretization error caused by the upwind expression of the Couette (velocity) term, non-symmetric control volumes are used for discretization of the Reynolds equation, while for the elasticity equation the standard approach is used. A numerical method for the solution of the pressure and the film thickness profiles of elastohydrodynamically lubricated isothermal line contacts is presented. Results are presented for chosen typical parameters of a highly loaded contact. To show the formula efficiency, the convergence speed of both the presented discretization formula and a chosen comparative discretization formula (A.A. Lubrecht, Ph.D. Thesis, University of Twente, The Netherlands, 1987 and C.H. Venner, Ph.D. Thesis, University of Twente, The Netherlands, 1991) are checked. The results show that the presented formula gives better approximations of film thickness values for a given number of equidistant grid nodes. Moreover, the presented approach is probably suitable for more sophisticated cases, such as transient situations and elliptical contacts. © 1998 John Wiley & Sons, Ltd.     

A Stokes model with cavitation for the numerical simulation of hydrodynamic lubrication

We present a cavitation model based on the Stokes equation and formulate adaptive finite element methods for its numerical solution. A posteriori error estimates and adaptive algorithms are derived, and numerical examples illustrating the theory are supplied, in particular with comparison to the simplified Reynolds model of lubrication. Copyright © 2010 John Wiley & Sons, Ltd.     

Weak coupling of a Reynolds model and a Stokes model for hydrodynamic lubrication

The Reynolds model is a reduced Stokes model, valid for narrow lubrication regions. In order to be able to handle locally non‐narrow regions such as pits or grooves, often displaying rapid geometrical variations, there is a need to be able to transit to the more accurate Stokes model. A fundamental problem is how to couple the two models in a numerical simulation, preferably allowing for different meshes in the different domains. In this paper, we present a weak coupling method for Reynolds and Stokes models for lubrication computations, including the possibility of cavitation in the different regions. The paper concludes with a numerical example. Copyright © 2010 John Wiley & Sons, Ltd.     

A perturbation solution in the nonlinear theory of circular plates

In this paper, we analyzed some problems of nonlinear circular plates by means of perturbation method. The perturbation parameters chosen here are obtained from solving the equations and are not certain mechanical quantities given precedently. This is an extension of W. Z. Chien’s perturbation method, which uses the central deflection as the perturbation parameter.     

On the lubrication approximation for a class of viscoelastic fluids

We present a rigorous derivation of a dimensionally reduced Reynolds type equation for thin film flow lubrication of a class of viscoelastic fluids by employing a perturbation analysis on the upper-convected Maxwell model in natural orthogonal coordinates. This approximation accounts for the viscoelastic and curvature corrections to the classical Reynolds lubrication approximation. Comparison of our approximation with the classical Reynolds approximation suggests that viscoelasticity can have a significant influence on the lubrication characteristics, at least for certain values of the film thickness and of the eccentricity ratios of the journal bearing.     

A COMPLETE EXPRESSION OF THE ASYMPTOTIC SOLUTION OF DIFFERENTIAL EQUATION WITH A∩-TH ORDER TURNING POINT

A second order linear ordinary differential equation has been studied, and the complete expresson, of the formal uniformly valid asymptotic solutions to the equation near turning point is obtained by using extended Airy function.     

AN ANALYTICAL SOLUTION OF HEAT CONDUCTION ON A LOCALLY NONUNIFORMLY HEATED SURFACE OF A PLATE WITH FINITE THICKNESS

ＡＮＡＮＡＬＹＴＩＣＡＬＳＯＬＵＴＩＯＮＯＦＨＥＡＴＣＯＮＤＵＣＴＩＯＮＯＮＡＬＯＣＡＬＬＹＮＯＮＵＮＩＦＯＲＭＬＹＨＥＡＴＥＤＳＵＲＦＡＣＥＯＦＡＰＬＡＴＥＷＩＴＨＦＩＮＩＴＥＴＨＩＣＫＮＥＳＳ（王明锐）（靳辉）ＡＮＡＮＡＬＹＴＩＣＡＬＳＯＬＵＴＩ...     

Method of calculating surface disturbances over a point source and a dipole

Formulas for calculating the deviations of the free surface of a heavy fluid in steady flow past a point source and a point dipole are derived. Examples of numerical calculations made in accordance with these formulas are presented.     

Stick-slip analysis of a circular point contact between a rigid sphere and a flat unidirectional composite with cylindrical fibers

The stick-slip contact problem is investigated here when at least one of the contacting bodies behaves as an ideal composite material with long fibers perpendicular to the direction of movement. Cylindrical inhomogeneous inclusions within a homogeneous media and with axes parallel to the contact surface are considered. The Eshelby’s equivalent inclusion method is used to solve the problem numerically. Interactions between close inclusions are taken into account in the numerical procedure, as well as the coupling between the normal and tangential contact problems. It is found that the presence of heterogeneities in the vicinity of the surface contact affects significantly the contact pressure distribution and subsequently the distribution of shear and slip at the interface.     

Observations of acoustically generated cavitation bubbles within typical fluids applied to a scroll expander lubrication system

An experimental study to evaluate the dynamic performance of three different types of cavitation bubbles is conducted. An ultrasonic transducer submerged into the working fluids of a scroll expander is utilised to produce cavitation bubbles and a high speed camera device is used to capture their behaviour. Three critical regions around the ultrasonic source, between the source and the solid boundary, and across the solid boundary were observed. Experimental results revealed that refrigerant bubbles sustain a continuous oscillatory movement, referenced as “wobbling effect”, without regularly collapsing. Analytical results indicate the influence of several factors such as surface tension/viscosity ratio, Reynolds number and Weber number which interpret that particular behaviour of the refrigerant bubbles. Within the refrigerant environment the bubbles obtain large Reynolds numbers and low Weber numbers. In contrast, within the lubricant and the water environment Weber number is significantly higher and Reynolds number substantially lower. The bubble radius and velocity alterations are accurately calculated during the cavitation process. Lubricant bubbles achieve the highest jet velocity while refrigerant bubbles having the lowest jet velocity are not considered as a destructive mean of cavitation for scroll expander systems.     

Thermoelastic contact mechanics for a flat punch sliding over a graded coating/substrate system with frictional heat generation

The problem of thermoelastic contact mechanics for the coating/substrate system with functionally graded properties is investigated, where the rigid flat punch is assumed to slide over the surface of the coating involving frictional heat generation. With the coefficient of friction being constant, the inertia effects are neglected and the solution is obtained within the framework of steady-state plane thermoelasticity. The graded material exists as a nonhomogeneous interlayer between dissimilar, homogeneous phases of the coating/substrate system or as a nonhomogeneous coating deposited on the substrate. The material nonhomogeneity is represented by spatially varying thermoelastic moduli expressed in terms of exponential functions. The Fourier integral transform method is employed and the formulation of the current thermoelastic contact problem is reduced to a Cauchy-type singular integral equation of the second kind for the unknown contact pressure. Numerical results include the distributions of the contact pressure and the in-plane component of the surface stress under the prescribed thermoelastic environment for various combinations of geometric, loading, and material parameters of the coated medium. Moreover, in order to quantify and characterize the singular behavior of contact pressure distributions at the edges of the flat punch, the stress intensity factors are defined and evaluated in terms of the solution to the governing integral equation.     

Exact solution of external tangential contact problem for a transversely isotropic elastic half-space

Summary  The following mixed boundary-value problem for a transversely isotropic elastic half-space is considered. Arbitrary tangential displacements are prescribed at the exterior of a circle, while the interior of the circle is free of tangential stress, and the normal stress vanishes all over the boundary. The governing integral equation is solved exactly, in closed form, and in terms of elementary functions. The method of continuation of solutions previously published by the author has been used here. Several examples are considered. No similar results has been reported before, even in the case of an isotropic body. Received 8 May 2000; accepted for publication 20 July 2000     

再论刚体在固定面上纯滚动时接触点的加速度

应用点的速度合成定理和加速度合成定理,推导出刚体在固定曲面上作平面纯滚动时接触点的速度和加速度的计算公式.该方法易于理解.     

Contact Problem for a Rectangular Punch on the Porous Elastic Half-Space

The paper is concerned with a contact problem about rigid rectangular punch forced into a half-space made of a linear elastic isotropic material with voids. We use a Cowin–Nunziato model for the half-space, and reduce the problem to a double Fredholm integral equation of the first kind. Then we apply two different approaches, to solve this equation. The first one is based on a direct collocation numerical technique. The second method is asymptotic, and we use a small parameter that is the relative width of the punch. Finally, compliance of the punch is determined, and results of the two different methods are compared with each other, as well as with a Sivashinsky–Panek–Kalker solution. Mathematics Subject Classifications (2000) 74M15.     

Large deformation adhesive contact mechanics of circular membranes with a flat rigid substrate

We study the large deformation mechanics of contact and adhesion between an inflated hyperelastic membrane and a rigid substrate. The initial configuration of the membrane is flat and circular and is clamped at the edge. Two types of friction conditions between the membrane and the substrate are considered: frictionless and no-slip contact. We derive an exact expression for the energy release rate in terms of local variables at the contact edge, thus linking adhesion to the contact angle. Our model can account for the effects of fluid pressure for experiments performed in solution. We also extend our formulation to include surface tension. Numerical simulations for a neo-Hookean membrane are carried out to study the relation between applied pressure and contact area.     

Frictional contact problem for elastic-viscoplastic materials with thermal effect

A dynamic contact problem for elastic-viscoplastic materials with thermal effects is investigated. The contact is bilateral, and the friction is modeled with Tresca’s friction law with heat exchange. A variational formulation of the model is derived, and the existence of a unique weak solution is proved. The proofs are based on the classical result of nonlinear first order evolution inequalities, the equations with monotone operators, and the fixed point arguments. Finally, the continuous dependence of the solution on the friction yield limit is studied.     

A note on the unsteady boundary layers over a flat plate

The unsteady boundary layer over a semi-infinite flat plate was investigated in this paper. The flow involves the unsteady flow over a flat plate with leading edge accretion or ablation. The momentum boundary layer was further analyzed and it was shown that the leading edge ablation had a similar effect to the wall mass injection or upstream wall movement making the fluid blown away from the wall. The thermal boundary layer of the same flow was also studied. Results show that the leading edge accretion or ablation can greatly change the fluid motion and the heat transfer characteristics.     

考虑海底接触的钢悬链式立管触地点动力响应以及疲劳损伤分析

基于考虑接触的钢悬链式立管SCR(Steel Catenary Riser)触地点处的结构特性,分别采用了考虑管土分离的线性截断模型以及包含土体吸力效应的帽盖模型来描述P-y曲线。通过改变上端浮体的垂荡运动幅度、土体吸力系数以及海床刚度,对SCR触地点处的动力响应以及疲劳损伤特性进行了分析。分析结果表明,SCR触地点的垂向位移、弯矩、等效应力以及疲劳损伤均随着浮体垂荡运动幅度的增加而呈上升趋势。SCR触地点的垂向位移随着土体吸力系数的增大由高幅低频响应转变为低幅高频响应。SCR触地点的疲劳损伤随着海床刚度的增加呈现先稳定再增加再稳定的趋势。     

Closed-form solutions of the frictional sliding contact problem for a magneto-electro-elastic half-plane indented by a rigid conducting punch

This paper focuses on the study of a frictional sliding contact problem between a homogeneous magneto-electro-elastic material (MEEM) and a perfectly conducting rigid flat punch subjected to magneto-electro-mechanical loads. The problem is formulated under plane strain conditions. Using Fourier transform, the resulting plane magneto-electro-elasticity equations are converted analytically into three coupled singular integral equations in which the main unknowns are the normal contact stress, the electric displacement and the magnetic induction. An analytical closed-form solution is obtained for the normal contact stress, electric displacement and magnetic induction distributions. The main objective of this paper is to study the effect of the friction coefficient and the elastic, electric and magnetic coefficients on the surface contact pressure, electric displacement and magnetic induction distributions for the case of flat stamp profile.