A cellular automaton model for boundary friction of PEEK and PEEK6

Nowadays a common material for journal bearings is PEEK (Polyetheretherketon) which is increasingly used under boundary friction. A Cellular Automaton model is developed to describe the boundary layer dynamics of PEEK and its composite PEEK6 sliding against a steel surface. Whereas PEEK is a homogeneous synthetic material, PEEK6 contains also carbon fibres for stability and fillers working as solid lubricants. The automaton shows a representative area of the real surface. The processes in the interface are described by a set of rules based on physical assumptions and measurements. Based on these rules the simulations show the dependency of friction and wear on the load spectrum. The discrete simulation allows to observe the topographic development of the PEEK and PEEK6 surface as well as the build-up of a transfer film on the steel surface. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Influence of nano-SiO<Subscript>2</Subscript> and carbon fibers on the mechanical properties of POM composites

Polyoxymethylene/carbon fiber(POM/CF)composites containing nano-SiO₂ were prepared, and their mechanical properties were investigated. At a content of 1-5 vol.%, the nano-SiO₂ exerted an obvious reinforcing effect on POM, leading to an increase in the elastic modulus and stiffness of the composites.     

EPR study of ZnS:Mn2+ nanocrystals and pyrex glasses

Pyrex glasses with different ZnS: Mn²⁺ contents were prepared by melting method. It has been found that Mn ion may occupy two sites: (Mn²⁺)_sub, and (Mn²⁺)_int from photoluminescene (PL) and photoluminescence excitation (PLE) spectra. The results were confirmed by the further electron panmagnetic resonance (EPR) experiments and the three types of states (Mn²⁺)_sub, (Mn²⁺)_int,and Mn clusters were identified. It was observed that theg-factor and the hyperfine structure (HFS) constant increase with the decreasing size of nanocrystallite. This may result from hybridization of sp³ electron states of ZnS and 3d⁵ electron states of Mn by the effects of quantum confinement and the surface states. Project supported by the National Natural Science Foundation of China and Laboratory of Excited State Processes, Chinese Academy of Sciences.     

Convexity analysis in detecting a steel plant hidden global optimum

This case study demonstrates the value of classical analysis and to a lesser degree, system decomposition for finding a global optimum missed by a sequential linear programming scheme which converges to a non-global local minimum. The example is a 20 variable steelmaking problem in which the variable annual cost to be minimized is linear, as are all constraints except a non-convex one in each blast furnace. The sequential linear programming method gives a provenlocal minimum, although the non-convex nonlinearity prevents any proof of global optimality. The provenglobal minimum found here has a 4% lower cost. The local minimum costs only 0.2% per annum less than the rather flat global maximum, so the original local minimization only achieved about 5% of the economy possible. In the overall plant, the cost saving is over three million US$ (1972) annually.Symbol Name of variable H combined hot iron rate (X ₄ + X ₄) - r ₁,r ₂ sinter/iron ratio for BF1 and BF2 - u ₁,u ₂ unit composition cost variation for BF1 and BF2 - v ₁,v ₂ variable feed cost for BF1 and BF2 - v _b(H) total variable feed cost for both blast furnaces - v _s (H) total variable cost for both steel furnaces - x ₁ sintered iron ore rate into BF1 - x ₂ pelleted iron ore rate into BF1 - x ₃ coke rate into BF1 - X ₄ hot iron rate from BF1 - x ₅ sintered iron ore rate into BF2 - x ₆ pelleted iron ore rate into BF2 - x ₇ coke rate into BF2 - X ₈ hot iron rate from BF2 - x ₉ hot iron to basic oxygen furnace (BOF) - x ₁₀ home scrap to BOF - x ₁₁ bought scrap to BOF - x ₁₂ silicon carbide to BOF - x ₁₃ crude steel from BOF - x ₁₄ home scrap to open-hearth furnace (OH) - x ₁₅ bought scrap to OH - x ₁₆ hot iron to OH - x ₁₇ crude steel from OH - x ₁₈ total crude steel - x ₁₉ total home scrap - x ₂₀ total bought scrap - Y ₁,Y ₂ additional hot iron from BF1 and BF2     

一种考虑聚醚醚酮（PEEK）不同力学状态的本构模型

聚醚醚酮（简称PEEK）以其优良的性能而广泛应用于高端机械、 核工程和航空等科技领域.为了描述其在应变、应变率和温度3种因素作用下的力学行为,依据PEEK在不同温度下呈现的3种力学状态,在著名的JC(Johnson Cook)本构模型的基础上,提出了针对高分子不同力学状态的分段JC本构模型.与传统JC模型及文献中改进JC模型相比,提出的分段JC模型能够更精确地表征PEEK在中高温下的力学行为,为PEEK在复合材料中的应用和分析奠定了理论基础.     

Tensile and tribological properties of a short-carbon-fiber-reinforced peek composite doped with carbon nanotubes

The main objective of this paper is to develop a high-wear-resistant short-carbon-fiber-reinforced polyetheretherketone (PEEK) composite by introducing additional multiwall carbon nanotubes (MWCNTs) into it. The compounds were mixed in a Haake batch mixer and fabricated into sheets by compression molding. Samples with different aspect ratios and concentrations of fillers were tested for wear resistance. The worn surfaces of the samples were examined by using a scanning electron microscope (SEM), and the photomicrographs revealed a higher wear resistance of the samples containing the additional carbon nanotubes. Also, a better interfacial adhesion between the short carbon fibers and vinyl ester in the composite was observed.     

Optimization of the composition and tribological properties of high-density polyethylene-calcite-silicon nitride composites by the method of experiment planning

The tribological characteristics (wear resistance, coefficient of friction ) of a high-density-polyethylene-base composite filled with calcite and highly disperse silicon nitride produced by the plasmochemical method are investigated experimentally. The experiment plan was compiled in the form of a simplex lattice, and new points were planned in conducting the experiments. Compositions possessing appreciably elevated wear resistance (by a factor of 500) and a coefficient of friction reduced by 20% as compared with the unfilled polymer were obtained. Institute of Inorganic Chemistry of the Latvian Academy of Sciences, Salasplis, LV-2169. Institute of Polymer Mechanics of the Latvian Academy of Sciences, Riga, LV-1006. Riga Mechanical University, Riga, LV-1050, Latvia. Translated from Mekhanika Kompozinykh Materialov, No. 5, pp. 690–695, September–October, 1996.     

Isoperimetric problems for convex bodies and a localization lemma

We study the smallest number ψ(K) such that a given convex bodyK in ℝ ⁿ can be cut into two partsK ₁ andK ₂ by a surface with an (n−1)-dimensional measure ψ(K) vol(K ₁)·vol(K ₂)/vol(K). LetM ₁(K) be the average distance of a point ofK from its center of gravity. We prove for the “isoperimetric coefficient” that

Kinetics of oxidation of deoxybenzoin by chromic acid

The kinetics of the oxidation of deoxybenzoin by chromic acid in 95% (vol/vol) aqueous acetic acid has been investigated. The reaction rate is first order with respect to the oxidant as well as to the organic substrate. The reaction rate decreases in the presence of added Mn (II) ions. The presence of complexing agents like succinic acid, piperidine, etc. decreases the rate. The thermodynamic parameters for the oxidation have been computed. A mechanism proceeding through an enol intermediate has been suggested.     

A sharp threshold for minimum bounded-depth and bounded-diameter spanning trees and Steiner trees in random networks

In the complete graph on n vertices, when each edge has a weight which is an exponential random variable, Frieze proved that the minimum spanning tree has weight tending to ζ(3) = 1/1³ + 1/2³ + 1/3³ +… as n → ∞. We consider spanning trees constrained to have depth bounded by k from a specified root. We prove that if k ≥ log₂ logn+ω(1), where ω(1) is any function going to ∞ with n, then the minimum bounded-depth spanning tree still has weight tending to ζ(3) as n → ∞, and that if k < log₂ logn, then the weight is doubly-exponentially large in log₂ logn ? k. It is NP-hard to find the minimum bounded-depth spanning tree, but when k≤log₂ logn?ω(1), a simple greedy algorithm is asymptotically optimal, and when k ≥ log₂ logn+ω(1), an algorithm which makes small changes to the minimum (unbounded depth) spanning tree is asymptotically optimal. We prove similar results for minimum bounded-depth Steiner trees, where the tree must connect a specified set of m vertices, and may or may not include other vertices. In particular, when m=const×n, if k≥log₂ logn+ω(1), the minimum bounded-depth Steiner tree on the complete graph has asymptotically the same weight as the minimum Steiner tree, and if 1 ≤ k ≤ log₂ logn?ω(1), the weight tends to $(1 - 2^{ - k} )\sqrt {8m/n} \left[ {\sqrt {2mn} /2^k } \right]^{1/(2^k - 1)}$ in both expectation and probability. The same results hold for minimum bounded-diameter Steiner trees when the diameter bound is 2k; when the diameter bound is increased from 2k to 2k+1, the minimum Steiner tree weight is reduced by a factor of $2^{1/(2^k - 1)}$ .     

Multirectangular characteristic invariants for power ?-Köthe spaces of first type

Let ? be a Banach sequence space with a monotone norm ‖⋅?_‖, in which the canonical system (ei) is a normalized unconditional basis. We consider the problem of quasi-diagonal isomorphism of first type power ?-Köthe spaces E?(λ,a) (see (1) below). From [P.A. Chalov, V.P. Zahariuta, On quasi-diagonal isomorphism of generalized power spaces, in: Linear Topological Spaces and Complex Analysis, vol. 2, METU - TÜB?TAK, Ankara, 1995, pp. 35-44; P.A. Chalov, T. Terzio?lu, V.P. Zahariuta, First type power Köthe spaces and m-rectangular invariants, in: Linear Topological Spaces and Complex Analysis, vol. 3, METU - TÜB?TAK, Ankara, 1997, pp. 30-44; P.A. Chalov, T. Terzio?lu, V.P. Zahariuta, Multirectangular invariants for power Köthe spaces, J. Math. Anal. Appl. 297 (2004) 673-695] it is known that the system of all m-rectangle characteristics μm (see (9) below) is a complete quasi-diagonal invariant on the class of all first type power Köthe spaces [V.P. Zahariuta, On isomorphisms and quasi-equivalence of bases of power Köthe spaces, Soviet Math. Dokl. 16 (1975) 411-414; V.P. Zahariuta, Linear topologic invariants and their applications to isomorphic classification of generalized power spaces, Turkish J. Math. 20 (1996) 237-289], if the relation of equivalency of systems and is defined by some natural estimates with constants independent of m. Deriving the characteristic from the characteristic β (see [V.P. Zahariuta, Linear topological invariants and isomorphisms of spaces of analytic functions, in: Matem. Analiz i ego Pril., vol. 2, Rostov Univ., Rostov-on-Don, 1970, pp. 3-13 (in Russian), in: Matem. Analiz i ego Pril., vol. 3, Rostov Univ., Rostov-on-Don, 1971, pp. 176-180 (in Russian); V.P. Zahariuta, Generalized Mityagin invariants and a continuum of mutually nonisomorphic spaces of analytic functions, Funktsional. Anal. i Prilozhen. 11 (1977) 24-30 (in Russian); V.P. Zahariuta, Compact operators and isomorphisms of Köthe spaces, in: Aktualnye Voprosy Matem. Analiza, vol. 46, Rostov Univ., Rostov-on-Don, 1978, pp. 62-71 (in Russian); P.A. Chalov, P.B. Djakov, V.P. Zahariuta, Compound invariants and embeddings of Cartesian products, Studia Math. 137 (1) (1999) 33-47; P.B. Djakov, M. Yurdakul, V.P. Zahariuta, Isomorphic classification of Cartesian products, Michigan Math. J. 43 (1996) 221-229; V.P. Zahariuta, Linear topologic invariants and their applications to isomorphic classification of generalized power spaces, Turkish J. Math. 20 (1996) 237-289], and using the S. Krein's interpolation method of analytic scale, we are able to generalize some results of [P.A. Chalov, V.P. Zahariuta, On quasi-diagonal isomorphism of generalized power spaces, in: Linear Topological Spaces and Complex Analysis, vol. 2, METU - TÜB?TAK, Ankara, 1995, pp. 35-44; P.A. Chalov, T. Terzio?lu, V.P. Zahariuta, First type power Köthe spaces and m-rectangular invariants, in: Linear Topological Spaces and Complex Analysis, vol. 3, METU - TÜB?TAK, Ankara, 1997, pp. 30-44; P.A. Chalov, T. Terzio?lu, V.P. Zahariuta, Multirectangular invariants for power Köthe spaces, J. Math. Anal. Appl. 297 (2004) 673-695].     

Two-sided bounds for the volume of right-angled hyperbolic polyhedra

For a compact right-angled polyhedron R in Lobachevskii space ?³, let vol(R) denote its volume and vert(R), the number of its vertices. Upper and lower bounds for vol(R) were recently obtained by Atkinson in terms of vert(R). In constructing a two-parameter family of polyhedra, we show that the asymptotic upper bound 5v ₃/8, where v ₃ is the volume of the ideal regular tetrahedron in ?³, is a double limit point for the ratios vol(R)/ vert(R). Moreover, we improve the lower bound in the case vert(R) ≤ 56.     

Influence of mechanical activation,ion implantation,and filler type on the formation of a transfer film in tribounits of UHMWPE-based composites

The supermolecular structure of composites obtained by reinforcing an ultrahigh-molecular-weight polyethylene with C and Al₂O₃ nanofibers, Cu and SiO₂ nanoparticles, and Al₂O₃ and AlO (OH) microparticles has been studied by means of X-ray diffraction analysis, infrared spectroscopy, and optical and electron microscopy. It is shown that the filler type (nano-, submicro-, or micro-) determines the character of the supermolecular structure, the evolution of friction transfer films, and the wear resistance of the composites.     

Numerical evaluation of zirconium reinforced aluminium matrix composites for sustainable environment

Due to the momentous advantages of composite materials, recent years many studies focused on reinforcing different new materials to the existing ones to improve their conventional strength and life time within the concern of application status. In the row, reinforcements on Al6061 become a fancy topic among researchers due to its wide applications including automobiles, yachts, electrical fittings and so on. This study continues this innovation by reinforcing three different reinforcement materials including zirconia (ZrO₂), zirconia + aluminium oxide (ZrO₂ +Al₂O₃) and fused zirconia aluminum (40FZA). These three reinforcing materials are included with the proposition of varying particle reinforcements as 5, 10 and 15%. The testing specimens were experimented to explore its mechanical, wear and corrosion behavior. Further the experimental results are given as inputs to the numerical analysis, PROMETHEE. By combining the experimental and numerical methodologies the reliability of the results were improved. However, from this study it can be evident that inclusion of 15% particle reinforcement of zirconia fused alumina in Al6061 provides greater strength, toughness, high resistance to wear and corrosion on both experimental and numerical analysis. There is ample room that this proposed material inclusion be a better option for the reinforcement of Al6061 among available alternatives for sustainable development.

     

Artificial Intelligence in numerical modeling of nano sized ceramic particulates reinforced metal matrix composites

Artificial neural network models have the capacity to eliminate the need for expensive experimental investigation in various areas of manufacturing processes, including the casting methods. An understanding of the inter-relationships between input variables is essential for interpreting the sensitivity data and optimizing the design parameters. Aluminum is the best metal for producing metal matrix composites which are known as one of the most useful and high-tech composites in our world. Combining aluminum and nano Al₂O₃ particles will yield a material with high mechanical and tribological properties. In this investigation, the accuracy of various artificial neural network training algorithms in FEM modeling of Al₂O₃ nano particles reinforced A356 matrix composites has been studied.     

Backward uniqueness of the s.c. semigroup arising in parabolic-hyperbolic fluid-structure interaction

A 2-d or 3-d fluid-structure interaction model in its linear form is considered, for which semigroup well-posedness (with explicit generator) was recently established in [G. Avalos, R. Triggiani, The coupled PDE-system arising in fluid-structure interaction. Part I: Explicit semigroup generator and its spectral properties, in: Fluids and Waves, in: Contemp. Math., vol. 440, Amer. Math. Soc., 2007, pp. 15-55; G. Avalos, R. Triggiani, The coupled PDE-system arising in fluid-structure interaction. Part II: Uniform stabilization with boundary dissipation at the interface, Discrete Contin. Dyn. Syst., in press]. This is a system which couples at the interface the linear version of the Navier-Stokes equations with the equations of linear elasticity (wave-like). In this paper, we establish a backward uniqueness theorem for such a parabolic-hyperbolic coupled PDE system. If {eAt}_t?0 is the (contraction) s.c. semigroup describing its evolution on the finite energy space H, then eATy₀=0 for some T>0 and y₀∈H, implies y₀=0. This property has implications in establishing unique continuation and controllability properties, as in the case of thermoelastic equations [M. Eller, I. Lasiecka, R. Triggiani, Simultaneous exact/approximate boundary controllability of thermoelastic plates with variable coefficient, in: Marcel Dekker Lect. Notes Pure Appl. Math., vol. 216, February 2001, pp. 109-230, invited paper for the special volume entitled Shape Optimization and Optimal Designs, J. Cagnol, J.P. Zolesio (Eds). (Preliminary version is in invited paper in: A.V. Balakrishnan (Ed.), Semigroup of Operators and Applications, Birkhäuser, 2000, pp. 335-351.); M. Eller, I. Lasiecka, R. Triggiani, Simultaneous exact/approximate boundary controllability of thermoelastic plates with variable thermal coefficient and moment control, J. Math. Anal. Appl. 251 (2000) 452-478; M. Eller, I. Lasiecka, R. Triggiani, Simultaneous exact/approximate boundary controllability of thermoelastic plates with variable thermal coefficient and clamped controls, Discrete Contin. Dyn. Syst. 7 (2) (2001) 283-301].     

Upper bound for the product of nonhomogeneous linear forms

It is proved that for any unimodular lattice Λ with homogeneous minimum L>0 and any set of real numbers α₁, α₂,..., α_n there exists a point (y₁, y₂,..., y_n) of Λ such that $$\Pi _{1 \leqslant i \leqslant n} |y_i + \alpha _i | \leqslant 2^{ - n/2_\gamma n} (1 + 3L^{8/(3n)/(\gamma ^{2/3} - 2L^{8/(3n)} )} )^{ - n/2} ,$$ where γⁿ= n^n/(n?1).     

Optimization of reliability and longevity of cylindrical shells subject to corrosive wear

The problem of the optimal (with respect to the minimum average rate of weight loss in a structure) design of a smooth cylindrical shell loaded by an axial compressive force and under corrosive wear, the rate of which depends exponentially on the stresses, is solved. The problem is solved analytically using apparatus of the method of Lagrange multipliers.Translated from Matematicheskie Metody i Fiziko-mekhanicheskie Polya, No. 26, pp. 59–63, 1987.     

On the Convergence of Sequences of Rational Approximations to Analytic Functions of a Certain Class

Complex analytic methods based on the theory of Walsh (1935)and on properties of orthonormal polynomials with general weight-functionon [–1, 1] are applied to the construction of variousrational approximations on the interval [–k, k] to a functiong(x) defined by or by where Remainder estimates are obtained, and from these, in the caseswhere g(x) is real on [–k, k], an asymptotic formula isobtained for the maximum error of the best rational approximationin the sense of the uniform norm. It is also shown that therate of convergence of the sequence of best approximations ofdegree n is twice the minimum rate predicted by Walsh's theory,in the sense that the degree of the approximation required fora given precision is approximately only half as great. Graphs are shown which illustrate that, for a simple example,the remainder estimates on which this asymptotic formula isbased are remarkably accurate even for approximations of lowdegree.     

Adaptive minimax testing in the discrete regression scheme

We consider the problem of testing hypotheses on the regression function from n observations on the regular grid on [0,1]. We wish to test the null hypothesis that the regression function belongs to a given functional class (parametric or even nonparametric) against a composite nonparametric alternative. The functions under the alternative are separated in the L₂-norm from any function in the null hypothesis. We assume that the regression function belongs to a wide range of Hölder classes but as the smoothness parameter of the regression function is unknown, an adaptive approach is considered. It leads to an optimal and unavoidable loss of order Open image in new window in the minimax rate of testing compared with the non-adaptive setting. We propose a smoothness-free test that achieves the optimal rate, and finally we prove the lower bound showing that no test can be consistent if in the distance between the functions under the null hypothesis and those in the alternative, the loss is of order smaller than the optimal loss.