Fast algorithm for the cutting angle method of global optimization

The cutting angle method for global optimization was proposed in 1999 by Andramonov et al. (Appl. Math. Lett. 12 (1999) 95). Computer implementation of the resulting algorithm indicates that running time could be improved with appropriate modifications to the underlying mathematical description. In this article, we describe the initial algorithm and introduce a new one which we prove is significantly faster at each stage. Results of numerical experiments performed on a Pentium III 750 Mhz processor are presented.

The generation of new high-angle boundaries in aluminium during hot torsion

The crystallographic rotation field for deformation in torsion is such that it is possible for orientations close to stable orientations to rotate away from the stable orientation. A Taylor type model was used to demonstrate that this phenomenon has the potential to transform randomly generated low-angle boundaries into high-angle boundaries. After imposing an equivalent strain of 1.2, up to 40% of the simulated boundaries displayed a disorientation in excess of 15°. These high-angle boundaries were characterised by a disorientation axis close to parallel with the sample radial direction. A series of hot torsion tests was carried out on 1050 aluminium to seek evidence for boundaries formed by this mechanism. A number of deformation-induced high-angle boundaries were identified. Many of these boundaries showed disorientation axes and rotation senses similar to those seen in the simulations. Between 10% and 25% of all the high-angle boundary present in samples twisted to equivalent strains between 2 and 7 could be attributed to the present mechanism.

Predicting molecular structures: an application of the cutting angle method

The ability to predict molecular geometries has important applications in chemistry. Specific examples include the areas of protein space structure elucidation, the investigation of host–guest interactions, the understanding of properties of superconductors and of zeolites. This prediction of molecular geometries often depends on finding the global minimum or maximum of a function such as the potential energy. In this paper, we consider several well-known molecular conformation problems to which we apply a new method of deterministic global optimization called the cutting angle method. We demonstrate that this method is competitive with other global optimization techniques for these molecular conformation problems.

Reducing yarn hairiness with a modified yarn path in worsted ring spinning

The spinning geometry of a ring frame plays an important role, and the twist triangle is the critical region in ring spinning. Changes in the spinning geometry may affect yarn properties. This paper examines the idea of ring spinning with a "diagonal" yarn path, and the effect of such a path on yam properties, particularly hairiness. Both "left diagonal" and "right diagonal" yam arrangements are tried on a 24-spindle Cognetex FLC worsted ring frame. The hairiness results obtained from the Zweigle hairiness meter show that the right diagonal yam path produces yams of lower hairiness than the conventional ring spun yarn in almost all the hair length groups. Yam evenness and tenacity are not as sensitive to the change in yarn path. The mean spindle speed at break is also tested, and there is some deterioration in spinning efficiency with the right diagonal yarn path, particularly at higher spinning speeds. Results from this study may help explain variations in yarns spun on poorly aligned ring frames.

Geometry and combinatorics of the cutting angle method

Lower approximation of Lipschitz functions plays an important role in deterministic global optimization. This article examines in detail the lower piecewise linear approximation which arises in the cutting angle method. All its local minima can be explicitly enumerated, and a special data structure was designed to process them very efficiently, improving previous results by several orders of magnitude. Further, some geometrical properties of the lower approximation have been studied, and regions on which this function is linear have been identified explicitly. Connection to a special distance function and Voronoi diagrams was established. An application of these results is a black-box multivariate random number generator, based on acceptance-rejection approach.

Cutting angle method - a tool for constrained global optimization

Cutting angle method (CAM) is a deterministic global optimization technique applicable to Lipschitz functions f: Rn → R. The method builds a sequence of piecewise linear lower approximations to the objective function f. The sequence of solutions to these relaxed problems converges to the global minimum of f. This article adapts CAM to the case of linear constraints on the feasible domain. We show how the relaxed problems are modified, and how the numerical efficiency of solving these problems can be preserved. A number of numerical experiments confirms the improved numerical efficiency.

Minimizing energy consumption of yarn winding in ring spinning

Ring spinning has been and will continue to be an important system for making staple yarns from different fibers in the textile industry. But high power consumption and low productivity remain the two outstanding problems with ring spinning. Based on an analysis of power distribution during yarn winding in ring spinning, models for the ratio of energy consumption to yarn production over a full yarn package are established. Spindle speed, yarn count, and package diameter are the three key parameters affecting this ratio. The effects on energy consumption of these parameters are discussed through a case study. The energy-to-production ratio increases with increased package diameter but decreases with increased spindle speed and/or yarn count (tex). The results will help guide spinners in minimizing energy consumption in ring spinning.

Distribution of power requirements during yarn winding in ring spinning

A model of a yam package is established for a ring spinning system. The yarn layer, surface area, and mass of the yam package are formulated with respect to the diameters of the empty bobbin and full yarn package, yarn count, and yarn winding-on time. Based on the principles of dynamics and aerodynamics, models of the power requirements for overcoming the skin friction drag, increasing the kinetic energy of the yarn package (bobbin and wound yarn), and overcoming the yarn wind-on tension are developed. The skin friction coefficient on the surface of a rotating yam package is obtained from experiment. The power distribution during yam packaging is discussed based on a case study. The results indicate that overcoming the skin friction drag during yarn winding consumes the largest amount of energy. The energy required to overcome the yarn wind-on tension is also significant.

Skin friction coefficient on a yarn package surface in ring spinning

The skin friction coefficient on the surface of a rotating yarn package affects the power required to drive the package. This paper examines the relationship between the skin friction coefficient on the package surface and its diameter and rotating speed, based on the fundamentals of aerodynamics and the experimental results of power consumption. Skin friction coefficients on the surfaces of an airplane, car top, and yarn package are discussed. The results indicate that the skin friction coefficient on the package surface without hairiness depends on the package diameter and spindle speed only. The skin friction coefficient on the yarn package surface is about three times that on the top surface of a car, and is about twenty times that on an airplane surface. The power consumed to overcome skin friction drag is more than that consumed to drive the spindle if the spindle speed is very slow. However, the situation reverses when the spindle speed is fast.

Predicting worsted spinning performance with an artificial neural network model

For a given fiber spun to pre-determined yarn specifications, the spinning performance of the yarn usually varies from mill to mill. For this reason, it is necessary to develop an empirical model that can encompass all known processing variables that exist in different spinning mills, and then generalize this information and be able to accurately predict yarn quality for an individual mill. This paper reports a method for predicting worsted spinning performance with an artificial neural network (ANN) trained with backpropagation. The applicability of artificial neural networks for predicting spinning performance is first evaluated against a well established prediction and benchmarking tool (Sirolan YarnspecTM). The ANN is then subsequently trained with commercial mill data to assess the feasibility of the method as a mill-specific performance prediction tool. Incorporating mill-specific data results in an improved fit to the commercial mill data set, suggesting that the proposed method has the ability to predict the spinning performance of a specific mill accurately.

An experimental investigation of yarn tension in simulated ring spinning

Yarn tension is a key factor that affects the efficiency of a ring spinning system. In this paper, a specially constructed rig, which can rotate a yarn at a high speed without inserting any real twist into the yarn, was used to simulate a ring spinning process. Yarn tension was measured at the guide-eye during the simulated spinning of different yarns at various balloon heights and with varying yarn length in the balloon. The effect of balloon shape, yarn hairiness and thickness, and yarn rotating speed, on the measured yarn tension, was examined. The results indicate that the collapse of balloon shape from single loop to double loop, or from double loop to triple etc, lead to sudden reduction in yarn tension. Under otherwise identical conditions, a longer length of yarn in the balloon gives a lower yarn tension at the guide-eye. In addition, thicker yarns and/or more hairy yarns generate a higher tension in the yarn, due to the increased air drag acting on the thicker or more hairy yarns.

An investigation of yarn snarling and balloon flutter instabilities in ring spinning

This article reports theoretical and experimental investigation on yarn snarling and balloon fluttering in ring spinning. Yarn snarling and balloon fluttering affect yarn breakage in ring spinning. The theoretical model has incorporated the tangential component of air drag on a ballooning yarn, which was ignored in previous models. The results show that yarn snarling happens in the balloon when the ratio of yarn length in the balloon to balloon height is greater than a specific value that depends on the yarn type and count. Yarn tension experiences an obvious change before and after yarn snarling. The balloon flutter appears between normal balloons while the balloon loops are changing. Fluttering balloon shapes that oscillate periodically between two and three loop configurations as yarn tension varies periodically have also been observed experimentally.

The effect of yarn hairiness on air drag in ring spinning

Air drag on yarn and package surfaces affects yarn tension, which in turn affects energy consumption and ends-down in ring spinning. This study investigated the effects of yarn hairiness on air drag in ring spinning. Theoretical models of skin friction coefficient on the surface of rotating yarn packages were developed. The predicted results were verified with experimental data obtained from cotton and wool yarns. The results show that hairiness increases the air drag by about one-quarter and one-third for the rotating cotton and wool yarn packages, respectively. In addition, yarn hairiness increases the air drag by about one-tenth on a ballooning cotton yarn.

Simulation and experimental validation of a ring spinning process

Ring spinning is the most important system of making high quality yarns in the textile industry. Yarn tension affects yarn breakage, which in turn affects yarn productivity in ring spinning. Accurate information about how various spinning parameters affect yarn tension is essential for the optimisation of the ring spinning process. In this paper, a program to simulate the ring spinning process was developed using MATLAB, which can predict yarn tension under given spinning conditions. The simulation results were verified with experimental results obtained from ring spinning cotton and wool yarns.