Product quality inspection in Bernoulli lines: analysis,bottlenecks, and design

This paper is devoted to serial production lines consisting of producing and inspection machines that obey the Bernoulli reliability and Bernoulli quality models. Such production lines are encountered in automotive assembly and painting operations where the downtime is relatively short and the defects are due to uncorrelated random events. For these systems, this paper develops analytical methods for performance analysis, bottleneck identification, and design. In addition, insights into the nature of bottlenecks in such systems are provided, and an empirical rule for placing an inspection machine that maximises the production rate of non-defectives is formulated.     

High Diffusion Permeability of Anion-Exchange Membranes for Ammonium Chloride: Experiment and Modeling

It is known that ammonium has a higher permeability through anion exchange and bipolar membranes compared to K⁺ cation that has the same mobility in water. However, the mechanism of this high permeability is not clear enough. In this study, we develop a mathematical model based on the Nernst–Planck and Poisson’s equations for the diffusion of ammonium chloride through an anion-exchange membrane; proton-exchange reactions between ammonium, water and ammonia are taken into account. It is assumed that ammonium, chloride and OH⁻ ions can only pass through membrane hydrophilic pores, while ammonia can also dissolve in membrane matrix fragments not containing water and diffuse through these fragments. It is found that due to the Donnan exclusion of H⁺ ions as coions, the pH in the membrane internal solution increases when approaching the membrane side facing distilled water. Consequently, there is a change in the principal nitrogen-atom carrier in the membrane: in the part close to the side facing the feed NH₄Cl solution (pH < 8.8), it is the NH₄⁺ cation, and in the part close to distilled water, NH₃ molecules. The concentration of NH₄⁺ reaches almost zero at a point close to the middle of the membrane cross-section, which approximately halves the effective thickness of the diffusion layer for the transport of this ion. When NH₃ takes over the nitrogen transport, it only needs to pass through the other half of the membrane. Leaving the membrane, it captures an H+ ion from water, and the released OH⁻ moves towards the membrane side facing the feed solution to meet the NH₄⁺ ions. The comparison of the simulation with experiment shows a satisfactory agreement.     

Spontaneous formation of arrays of three-dimensional islands in epitaxial layers

An analysis is made of a theoretical model of the formation of three-dimensional nanometer-size islands in molecular beam epitaxy. The kinetics of the self-organization processes are described using a lattice gas model of the adsorbate with self-consistent allowance for lateral interactions in the activation energies of the diffusion processes. It is shown that at below-critical temperatures in a certain range of thicknesses, decay of the spatially uniform state gives rise to arrays of three-dimensional nano-islands which do not participate in the coalescence process after growth has ceased. The average size of the islands, their geometric profile, and the spatial ordering depend strongly on the kinetic parameters of the model. Pis’ma Zh. Tekh. Fiz. 24, 20–26 (July 12, 1998)     

Energy-Based Micromechanics Analysis on Fatigue Crack Propagation Behavior in Sn-Ag Eutectic Solder

Sn-Ag-eutectic-based solders are replacing Sn-Pb eutectic solders in the electronics industry. The current paper extends the recently developed approach based on phase transformation theory, micromechanics, and fracture mechanics to treat fatigue crack nucleation and propagation for steels and alloys to predict fatigue crack propagation in solder alloys. To verify the proposed method, fatigue experiments were conducted on Sn-3.5Ag solder alloys. Finite element analysis is performed to predict the stress intensity factor range ΔK and the required energy U to increase the crack by a unit area. Unified creep-plasticity theory and a cohesive zone model are incorporated to predict the creep and hysteresis effects on fatigue crack propagation in solder and the interfacial behavior between the solder alloy and the intermetallic layer, respectively. With U determined numerically, the predicted fatigue crack propagation rate using phase transformation theory is compared with experimental data for Sn-3.5Ag and Sn-37Pb eutectic solders. Reasonable agreement between theoretical predictions and experimental results is obtained.     

Buffer capacity for accommodating machine downtime in serial production lines

This paper investigates the smallest level of buffering (LB), necessary to ensure the desired production rate in serial lines with unreliable machines. The reliability of machines is assumed to obey either exponential, or Erlang, or Rayleigh models. The LB is measured in units of the average downtime, T down . The dependence of LB on the reliability model, the number of machines, M , the average uptime, T up , and the efficiency, e = T up /( T up + T down ) is analysed. It is shown that reliability models with larger coefficient of variation require larger LB, and an empirical law that connects LB of the exponential model with those for other reliability models is established. It is shown that LB is an increasing function of M , but with an exponentially decreasing rate, saturating at around M = 10. Also, it is shown that LB does not depend explicitly on T up and is a decreasing function of e . Based on these results, rules-of-thumb are provided for selecting buffer capacity, which guarantee sufficiently high line efficiency.     

Influence of diffusion annealing on residual resistivity of Nb3Sn-based chromium-plated strands obtained by a bronze process

The residual resistivity ratio, R₂₇₃/R₂₀, is an important parameter for multifilament superconductors (strands) based on Nb₃Sn that are used to manufature cables of magnetic systems. High values of RRR impart stability to the cable with regard to thermal excitations. Nb₃Sn strands for magnetic system of the International Thermonuclear Experimental Reactor are manufactured from high purity oxygen-free copper with RRR > 250 units; however, after extended diffusion annealing intended to form superconducting phase Nb₃Sn, the residual resistivity ratio values of the strands decrease. This work investigates the influence of diffusion annealing for 55?C200 h during the final stage at 650°C on the residual resistivity ratio of chromium-plated Nb₃Sn strands. The contents of chromium and oxygen have been analyzed using X-ray spectral microanalysis of the strand surface and peripheral copper layers. Mass spectrometry with inductively coupled plasma (ICP mass spectrometry) has been used to determine the total chromium content in the copper shell. The influence of chromium and oxygen diffusion from coating during annealing at 650°C on the residual resistivity ratio has been demonstrated. Based on the data of ICP mass spectrometry, the depth of the penetration of chromium in a copper shell has been assessed.     

Microstructure and properties of Nb<Subscript>3</Subscript>Sn superconductors for the magnet system of the international thermonuclear experimental reactor

Results of a study of promising Nb₃Sn superconductors fabricated with the use of a “bronze” method and a method of “internal source of tin” for toroidal coils of the magnet system of the international thermonuclear experimental reactor (ITER) are presented. The main structural parameters and factors of the process of manufacturing technical superconductors based on Nb₃Sn, which determine the superconducting properties, are analyzed. The current-carrying capacity and the losses to hysteresis are determined for conductors with various diameters. The structure of the layer of superconducting Nb₃Sn compound is studied, and the relation between the structural parameters and the superconducting properties of the developed conductors is described. Examples of Nb₃Sn superconductors with a reinforcing element from a nanocomposite alloy Cu - 18% Nb are presented. Strength characteristics of the reinforced conductors are studied. Prospects of further enhancement of superconducting properties of Nb₃Sn superconductors obtained by both methods are estimated.