Performance behaviour of elliptical-bore journal bearings lubricated with solid granular particulates

Journal bearings operating in hot environments and at high temperatures experience accelerated degradation of lubricating oils. In such situations, dry granular particulates have emerged as potential media for providing lubrication in journal bearings in place of lubricating oils. Granular particulates do not degrade thermally, even at considerably high temperatures. This work explores the static and dynamic performance characteristics of elliptical-bore journal bearings lubricated with granular particulates. It is found that a bearing lubricated with a larger size (2 μm) particles offers better performance compared with that using smaller size (1 μm) particles. Bore ellipticity reduces the load-carrying capacity and increases side leakage and the coefficient of friction; however, rotor stability is marginally improved at low eccentricity ratios (<0.6), followed by significant improvement at high eccentricity ratios (>0.6).     

Effects of the weak/micro-discontinuity of interface on the fracture behavior of a functionally graded coating with an inclined crack

The mechanical model was established for the anti-plane fracture problem of a functionally graded coating–substrate system with a coating crack inclined to the weak/micro-discontinuous interface. The Cauchy singular integral equation for the crack was derived using Fourier integral transform, and the Lobatto–Chebyshev collocation method put up by Erdogan and Gupta was used to get its numerical solution. Finally, the effects of the weak/micro-discontinuity of the interface on SIFs were analyzed, the “affected regions” corresponding to the two crack tips have been obtained and their engineering significance was discussed. It was indicated that, for the crack tip in the corresponding “affected region”, to reduce the weak-discontinuity of the interface and to make the interface micro-discontinuous are the two effective ways to reduce the SIF, and the latter way always has more remarkable SIF-reduction effect. For the crack tip outside the “affected region”, its SIF is mainly influenced by material stiffness, and to prevent such a tip from growing toward the interface “softer coating and stiffer substrate” is a more advantageous combination than “stiffer coating and softer substrate”.     

Skewness factor of turbulent velocity derivative

Using nonequilibrium statistical mechanics closure method, it is shown that the skewness factor of the velocity derivative of isotropic turbulence approaches a constant −0.515 when the Reynolds number is very high, which is in agreement with the DNS (direct numerical simulation) result of Vincent and Meneguzzi (1991). The project supported by the National Basic Research Program “Non-linear Science”     

Measure-theoretic foundations of statistical mechanics

The basic formulas of classical equilibrium statistical mechanics are derived from well-known theorems in measure theory and ergodic theory. The method used is a generalization of the methods of Khinchin and Grad and deals with several, in fact a “complete set”, of “invariants” or “integrals of the motion”. Most of the results are simple corollaries of Birkhoff's ergodic theorem, and since time-averages are used, the whole approach is characterized by an absence of statistical “ensembles” and probability notions. In the course of the development a “generalized temperature” is introduced, and a generalization of the second law of thermodynamics is derived. Formulas for the “microcanonical”, “canonical”, and “grand canonical” distributions appear as special cases of the general theory.     

Operator‐splitting method for the analysis of cavitation in liquid‐lubricated herringbone grooved journal bearings

This paper presents an operator‐splitting method (OSM) for the solution of the universal Reynolds equation. Jakobsson–Floberg–Olsson (JFO) pressure conditions are used to study cavitation in liquid‐lubricated journal bearings. The shear flow component of the oil film is first solved by a modified upwind finite difference method. The solution of the pressure gradient flow component is computed by the Galerkin finite element method. Present OSM solutions for slider bearings are in good agreement with available analytical and experimental results. OSM is then applied to herringbone grooved journal bearings. The film pressure, cavitation areas, load capacity and attitude angle are obtained with JFO pressure conditions. The calculated load capacities are in agreement with available experimental data. However, a detailed comparison of the present results with those predicted using Reynolds pressure conditions shows some differences. The numerical results showed that the load capacity and the critical mass of the journal (linear stability indicator) are higher and the attitude angle is lower than those predicted by Reynolds pressure conditions for cases of high eccentricities. Copyright © 2004 John Wiley & Sons, Ltd.     

电流变液滑动轴承的数值研究

基于油膜内屈服面位置可能出现的4种情况，Tichy提出了用于Bingham流体滑动轴承特性及其屈服面位置的计算方法，在将该计算方法推广到电流变液滑动轴承的计算时，发现随着外加电场强度的变形，出现了轴承风屈服面位置不变的非物理结果，而且Tichy的方法只能适用于无限宽滑动轴承，为了对有限宽度的电流变液滑动轴承进行数值研究，采用了类Bingham模型，通过差分离散和超松驰迭代的方法对雷诺方程进行求解，计算结果表明：电流变流滑动轴承内的压力分布可以通过外加电场强度来控制，轴承间隙内屈服面位置随电场强度变化而产生的移动是使轴承润滑性能得以改变的重要力学机制；在轴承以高剪切速率运转时，由于电流变液表观黏度随电场强度的变化已经很小，该机制在轴承的设计中尤为重要。     

Manufacturing tolerant topology optimization

In this paper we present an extension of the topology optimization method to include uncertainties during the fabrication of macro, micro and nano structures. More specifically, we consider devices that are manufactured using processes which may result in （uniformly） too thin （eroded） or too thick （dilated） structures compared to the intended topology. Examples are MEMS devices manufactured using etching processes, nano-devices manufactured using e-beam lithography or laser micro-machining and macro structures manufactured using milling processes. In the suggested robust topology optimization approach, under- and over-etching is modelled by image processing-based ＂erode＂ and ＂dilate＂ operators and the optimization problem is formulated as a worst case design problem. Applications of the method to the design of macro structures for minimum compliance and micro compliant mechanisms show that the method provides manufacturing tolerant designs with little decrease in performance. As a positive side effect the robust design formulation also eliminates the longstanding problem of one-node connected hinges in compliant mechanism design using topology optimization.     

Numerical investigation on the flowfield of ＂swallowtail＂ cavity for supersonic mixing enhancement

A ＂swallowtail＂ cavity for the supersonic combustor was proposed to serve as an efficient flame holder for scramjets by enhancing the mass exchange between the cavity and the main flow. A numerical study on the ＂swallow- tail＂ cavity was conducted by solving the three-dimensional Reynolds-averaged Navier-Stokes equations implemented with a k-e turbulence model in a multi-block mesh. Turbu- lence model and numerical algorithms were validated first, and then test cases were calculated to investigate into the mechanism of cavity flows. Numerical results demonstrated that the certain mass in the supersonic main flow was sucked into the cavity and moved spirally toward the combustor walls. After that, the flow went out of the cavity at its lateral end, and finally was efficiently mixed with the main flow. The comparison between the ＂swallowtail＂ cavity and the conventional one showed that the mass exchanged between the cavity and the main flow was enhanced by the lateral flow that was induced due to the pressure gradient inside the cavity and was driven by the three-dimensional vortex ring generated from the ＂swallowtail＂ cavity structure.     

Order reduction and nonlinear behaviors of a continuous rotor system

An isotropic flexible shaft, acted by nonlinear fluid-induced forces generated from oil-lubricated journal bearings and hydrodynamic seal, is considered in this paper. Dimension reductions of the rotor system were carried out by both the standard Galerkin method and the nonlinear Galerkin method. Numerical simulations provide bifurcation diagrams, spectrum cascade, orbits of the disk center and Poincaré maps, to demonstrate the dynamical behaviors of the system. The results reveal transitions, or bifurcations, of the rotor whirl from being synchronous to non-synchronous as the unstable speed is exceeded. The non-synchronous oil/seal whirl is a quasi-periodic motion. In the regime of quasi-periodic motion, the “windows” of multi-periodic motion were found. The investigation shows that the nonlinear Galerkin method has an advantage over the standard one with the same order of truncations, because the influences of higher modes are considered by the former.     

Studies on nonlinear stability of three-dimensional H-type disturbance

The three-dimensional H-type nonlinear evolution process for the problem of boundary layer stability is studied by using a newly developed method called parabolic stability equations (PSE). The key initial conditions for sub-harmonic disturbances are obtained by means of the secondaryinstability theory. The initial solutions of two-dimensional harmonic waves are expressed in Landau expansions. The numerical techniques developed in this paper, including the higher order spectrum method and the more effective algebraic mapping for dealing with the problem of an infinite region, increase the numerical accuracy and the rate of convergence greatly. With the predictor-corrector approach in the marching procedure, the normalization, which is very important for PSE method, is satisfied and the stability of the numerical calculation can be assured. The effects of different pressure gradients, including the favorable and adverse pressure gradients of the basic flow, on the “H-type“ evolution are studied in detail. The results of the three-dimensional nonlinear “H-type“ evolution are given accurately and show good agreement with the data of the experiment and the results of the DNS from the curves of the amplitude variation, disturbance velocity profile and the evolution of velocity.     

Numerical modeling of the dynamics of a viscous-fluid droplet

A numerical model developed on the basis of the level set method is proposed. This makes it possible to describe both the nonlinear oscillations of a single viscous-fluid droplet and the fragmentation and coalescence processes. The Navier-Stokes equations written in “velocity-pressure” variables on a rectangular uniform grid in cylindrical coordinates are solved using the method of splitting into physical processes. Non-oscillating solutions for two-phase media with a characteristic density ratio of less than 10⁻³ and Re > 1000 are obtained. The possibilities of the approach proposed are demonstrated with the reference to the problem of a droplet falling from a capillary (detachment from the capillary, formation of a “Plato ball”, droplet motion, collision with a plane wall, droplet oscillations on the wall, and droplet spreading). A comparison of the numerical results with the known calculation models and experimental data shows satisfactory agreement with respect to both the phases and the shape of the droplet.     

Design of a transversely layered cantilever of minimum mass under specified maximum-deflection constraint

The problem of optimal design of a transversely layered cantilever beam of minimum mass composed of a finite set of elastic homogeneous isotropic materials is considered for the case where a constraint is imposed on the maximum deflection of the beam and information on the loads applied to the beam is incomplete. It is shown that, among these loads, there exists the “worst” point load whose magnitude is equal to the resultant of the forces applied to the beam, for which the deflection is maximal for any material distribution along the beam. The necessary optimality conditions are obtained for the mass-minimization problem of the beam under the “worst” loading, a numerical algorithm is developed for the synthesis of the optimal cantilever, and a numerical example is given. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 48, No. 4, pp. 104–110, July–August, 2007.     

Statement of the two-body problem in the parameters of the extended Galilei group

The classical mechanical problem on the motion on a system of two or several bodies is stated in terms of parameters of the 13-parameter extended Galilean group (translations, rotations, boosts, and gravitational transformations) without using such traditional notions as “point” and “force.”     

Constructal Design of Vascular Porous Materials and Electrokinetic Mass Transfer

According to constructal theory, the “generation of flow configuration” is a universal phenomenon in physics. This phenomenon is covered by the constructal law: “For a finite-size flow system to persist in time (to live) it must evolve such that it provides greater and greater access to the currents that flow through it.” This paper shows how the constructal law can be used to (1) predict and explain features of “design” in nature, and (2) design effective strategies and configurations for engineering. Many natural flow designs rely on two flow mechanisms: channels with relatively low resistivity, interwoven with diffusion across the interstices. The “design” is the balance between the two mechanisms. The flow from line to line (or plane to plane) through a sufficiently fine porous medium encounters less resistance than the flow through parallel channels when it is configured as trees that alternate with upside down trees: from this follows the prediction that natural porous media (e.g., hill slope) should be multiscale (bidisperse) and non-uniformly distributed. A porous medium contaminated with ionic species is decontaminated the fastest when the ionic flow is configured as two flow mechanisms in balance: “channeling” driven by potential differences between optimally positioned electrodes, and diffusion driven by concentration differences across the interstices between the channels.     

Initial Conditions and Near-Field Dynamics in Turbulent Liquid Sheets

High-speed liquid “curtains” have been proposed to protect solid structures in fusion energy applications. Minimizing free-surface waves and spray formation in such flows is important for effective protection in this application. In this work, free-surface waves and turbulent breakup were studied experimentally in jets of water issuing from a rectangular nozzle into ambient air at a Reynolds number of 1.2 × 10⁵. Laser-Doppler anemometry was used to characterize the streamwise and transverse velocity components in the nozzle for two different flow calming section designs. Planar laser-induced fluorescence was used to measure the free-stream position in the near-field of the sheet. The results suggest that transverse velocity fluctuations in the nozzle are the primary factor in determining the amplitudes of free-surface waves. Removing a small amount of low-speed fluid immediately downstream of the nozzle exit (“boundary-layer cutting”) is shown to both significantly reduce free-surface waves and the amount of spray due to turbulent breakup. Overall, boundary-layer cutting appears to have the greatest benefit when used on a “well-conditioned” turbulent liquid sheet.     

The “Arch of equilibration” of Charles Hutton (1772)

This paper is a historical re-visitation of the work of C. Hutton, a mathematician of the XVIII century, who wrote an innovative essay on the shape of arches, whose intrados he identifies with the curve of pressure, that he names “arch of equilibration”. His solution was mostly ignored by his contemporaries and after the middle of the XIX century forgotten. But Hutton’s problem is important, also because it offers the first example of an inverse problem in structural mechanics.     

Numerical simulation of Mach reflections

In this paper, the “FLIC” difference method with triangular mesh is adopted to numerically simulate the regular and Mach reflections that occur when a shock wave pass around a wedge. The compuational result is compared with the shock tube experimental results of G. Ben-Dor and I. I. Glass. The comparison shows that the position, shape of shock wave and height of Mach stem all show a good agreement. Consequently, the “FLIC” difference method with triangular mesh is quite satisfactory in numerical simulation of the regular and Mach reflections.     

水润滑高速动静压轴承试验研究

研究了动静压轴承在水介质润滑和高速、高压极端工况条件下,最小液膜厚度和流量等性能参数的变化情况,并将其与理论预测结果进行比较.结果表明,水润滑动静压轴承在高速时能够稳定运行,且形成完整的润滑液膜,没有出现明显的汽化及汽蚀现象,试验后轴承表面涂层基本完好.试验结果显示出轴承的承载能力和流量主要取决于供水压力,这与理论预测结果基本一致.     

Stress analysis for an infinite strip weakned by periodic cracks

Stress analysis for an infinite stripcracks were assumed in a horizontal position,weakened by periodic cracks is studied. The and the strip was applied by tension “p“ in y-direction. The boundary value problem can be reduced into a complex mixed one. It is found that the EEVM ( eigenfunction expansion variational method) is efficient to solve the problem. The stress intensity factor at the crack tip and the T-stress were evaluated. From the deformation response under tension the cracked strip can be equivalent to an orthotropic strip without cracks. The elastic properties in the equivalent orthotropic strip were also investigated. Finally, numerical examples and results were given.     

Generation and registration of disturbances in a gas flow. 1. Formation of arrays of tubular microheaters and microsensors

A new method is proposed for creating “smart” surfaces for suppressing turbulence and retaining a laminar supersonic flow. Methods of formation of super-fast-response sensors and actuators for such surfaces are developed. Such sensors and actuators are structurally designed as microtubes made of SiO ₂ /Si ₃ N ₄ /Au and InGaAs/GaAs/Au heterofilms and suspended above a substrate; the wall thickness of these tubes is in the nanometer range; the tubes are connected to electrical contacts. Models of distributed arrays of tubular microsensors and microactuators are fabricated in a single technological process, which involves the well-established planar technology and the technology of rolling of stressed heterofilms. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 50, No. 2, pp. 145–151, March–April, 2009.