Modelling yarn balloon motion in ring spinning

Air-drag on a ballooning yarn and balloon shape affect the yarn tension and ends-down (yarn breakage), which in turn affects energy consumption and yarn productivity in ring spinning. In this article, a mathematical model of yarn ballooning motion in ring spinning is established. The model can be used to generate balloon shape and predict tension in the ballooning yarn under given spinning conditions. Yarn tension was measured using a computer data acquisition system and the balloon shapes were captured using a digital camera with video capability during the experiments using cotton and wool yarns at various balloon-heights and with varying yarn-length in the balloon. The air-drag coefficients on ballooning cotton and wool yarns in ring spinning were estimated by making a “best fit” between the theoretical and experimental turning points. The theoretical results were verified with experimental data. The effects of air-drag and balloon shape on yarn tension are discussed.     

Mathematical modeling and numerical simulation of yarn behavior in a modified ring spinning system

In the paper, yarn dynamical behavior and twist distribution in a modified ring spinning system are investigated. Equations of motion and twist wave propagation are used to obtain the numerical solutions of yarn path, yarn tension and twist distribution in steady state. It is observed that yarn path in the twisting zone has several classic modes corresponding to the yarn tension, and all of the yarn paths are approximately planar curves rather than spatial curves. The angular velocities of yarn at the twisting device are given as well as the twist of yarn in the modified ring spinning system. Experiments are conducted to evaluate the yarn paths and twist distributions under consideration. The theoretical and experimental results have a good agreement.     

基于泊松过程的理想纱条的数学建模与条干不匀分析

在Rao给出的理想纱条的数学定义的基础上,进一步提出利用泊松过程来描述纤维在理想纱条中的随机排列.由此得出纱条片段中纤维左头端数服从泊松分布,相邻纤维的左头端间隔距离服从指数分布,纤维左头端在纱条中的位置服从均匀分布,纱条截面的纤维根数服从泊松分布,这对理解纤维在纱条中的排列结构以及模拟纤维在纱条中的随机排列提供了基础.在此模型的基础上对纱条的条干不匀进行了分析,给出了考虑纤维细度因素之后的条干不匀公式.     

Using the fundamental equation of constrained motion with inequality constraints

In this paper we investigate a computational approach to keeping a moving particle within a predefined annulus or a predefined bounded space, formed by two concentric spheres with radii L_min and L_max, respectively, assuming that said particle cannot maintain a perfectly circular trajectory. The study develops an algorithm for dealing with a system in which constraints are expressed as inequalities. The proposed approach expresses the trajectory in terms of winding/unwinding logarithmic spirals with transitions, expressed as damped vibrations, between them. These transitions are necessary to resolve incompatibility between initial conditions for winding/unwinding spirals. Equations of motion for the particle are obtained by using the Fundamental Equation of Constrained Motion. The obtained simulation results show that such an approach produces the desired pseudo-periodic type of motion, and the particle stays within the predefined region of space for a long duration, although no cycle of its trajectory is repeated.     

A note on “Production lot sizing with quality screening and rework”

Recently, Moussawi-Haidar et al. (2016) considered a production process with random supply and an inspection process performed during and at the end of production. Two economic production quantity models with defective items were developed, in which Model 1 assumes that defective items are sold at a discounted price at the end of inspection process, and Model 2 assumes that defective items are reworked at a cost at the end of inspection process. In the paper, there are some mathematical expressions which are to be corrected. We first present the mathematical expressions corrected and establish the necessary conditions for which there is an optimal solution. We next provide the correct solutions to the numerical example.     

Wick–Itô formula for regular processes and applications to the Black and Scholes formula

We derive a Wick–Itô formula, that is, an Itô-type formula based on Wick integration. We derive it in the context of regular Gaussian processes which include Brownian motion and fractional Brownian motion with Hurst parameter greater than 1/2. We then consider applications to the Black and Scholes formula for the pricing of a European call option. It has been shown that using Wick integration in this context is problematic for economic reasons. We show that it is also problematic for mathematical reasons because the resulting Black and Scholes formula depends only on the variance of the process and not on its dependence structure.     

利用回归分析对正交试验结果进行修正

本文以纱线上浆率工艺参数正交试验为实例 ,利用回归分析的方法加以验证和修正 ,使工艺参数更符合实际情况 ,说明两种方法有较好的互补性 .     

新型纺纱胶辊的优化设计和现场生产管理

本文介绍应用实验设计法对纺纱工艺中主要牵伸元件胶辊配方进行抗干扰最优化设计及胶辊生产现场管理     

Natural oscillations of yarn balloons in ring spinning

Ring spinning is the most relevant production process for high quality short staple yarn. Recent technological advances using a twisting system involving frictionless superconducting magnetic bearings motivate a renewed interest in the dynamics of the process.A new deduction of the equations of motion for stationary and oscillatory movement is presented using Hamilton’s Principle of Least Action, taking into account axial transport, air drag and boundary conditions at the bearing. By application of Ritz’s method, system matrices are defined to enable the study of natural frequencies and mode shapes. These are validated by comparing to experimental results from literature, and case studies for industrially relevant parameter variations are performed.     

Asymptotic analysis of Poisson's equation in a thin domain and its application to thin-walled elastic beams and tubes

We study the limit behaviour of solution of Poisson's equation in a class of thin two-dimensional domains, both simply connected or single-hollowed, as its thickness becomes very small. The method is based on a transformation of the original problem into another posed on a fixed domain, obtention of a priori estimates and convergence results when thickness parameter tends to zero. As an important application of abstract results we obtain the limit expressions for functions appearing in elastic beam theories as torsion and warping functions. In this way, we provide a mathematical justification and a correct definition of torsion, warping and Timoshenko functions and constants that should be used in the open and closed thin-walled elastic beam theories. © 1998 by B. G. Teubner Stuttgart–John Wiley & Sons Ltd.     

Closed Hypersurfaces Driven by Mean Curvature and Inner Pressure

We introduce a hyperbolic equation that describes the motion of closed hypersurfaces in a Riemannian manifold with surface tension and inner pressure as driving forces. In the case of spherical surfaces this equation can be considered as an idealized mathematical model for a moving soap bubble. The equation is derived as an Euler‐Lagrange equation from a suitable action integral. It is a quasi‐linear degenerate hyperbolic PDE of second order that describes the motion of the surfaces extrinsically. Our main results are the solution of the Cauchy problem by means of the Nash‐Moser inverse function theorem, a continuation criterion, and stability estimates. © 2012 Wiley Periodicals, Inc.     

A Noise-Shaping Theorem

Noise shaping is a process which aims to remove as much quantization noise as possible from the spectrum of a given band-limited signal when quantizing it (recall that the spectrum of a signal is the support of its Fourier transform). We provide a mathematical analysis of such a process, using methods of harmonic analysis on the unit disc. We are especially interested in conditions under which an analytic (but not necessary polynomial) function may be used as a transfer function of the process. Stability conditions will be given under terms of metric characteristics of the transfer function (stability means that the quantizer is never overloaded). Several kinds of quantizer transfer functions will be considered, especially midtread and midriser ones. We shall restrict our analysis to the case of deterministic (i.e., not random) signals. Some knowledge of Fourier analysis and signal processing will be presupposed.     

The influence of water sorption-desorption cycles on the mechanical properties of composites based on recycled polyolefine and linen yarn production waste

The effect of water on the mechanical properties (tensile modulus, ultimate tensile strength, tensile strain, and specific work at break) of both chemically treated and untreated composites based on a recycled low-density polyethylene and linen yarn production waste is analyzed. It is found that three water sorption-desorption cycles change the tensile properties of both the materials irreversibly. This effect is considered as the result of partial fracture of the fiber-matrix interface. Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 43, No. 6, pp. 839–848, November–December, 2007.     

复数在鱼雷或舰船平面运动规律研究中的应用

为了更方便地研究鱼雷、水面舰船等武器或装备的平面运动规律,运用复数的指数表示,在相应坐标系下对它们的运动规律进行描述,得到任意时刻的轨迹方程,从而利用复数的运算性质和数学分析的方法进行分析,不仅能简单明确的描述问题,又能很大程度地省去了直角坐标系下繁琐的运算过程,还可以直接在MATLAB环境实现相关的结果,从而为平面运动规律问题的研究提供了的更为方便的工具和方法,尤其是对解决有关转角运动的问题意义更大.     

Geometry of warped product pseudo-slant submanifolds of Kenmotsu manifolds

In this paper, we study pseudo-slant submanifolds and their warped products in Kenmotsu manifolds. We obtain the necessary conditions that a pseudoslant submanifold is locally a warped product and establish an inequality for the squared norm of the second fundamental form in terms of the warping function. The equality case is also considered.     

A nonlinear dynamic model for a rotor-spun composite yarn spinning process

A nonlinear dynamic model is proposed for the rotor-spun composite yarn spinning process. The position of a convergent point and the section area can be easily determined using the proposed model. Trajectories and phase diagrams can be obtained for different spinning parameters.     

La preuve en mathématique

Proof and deductive method in mathematics have their origin in the classic model of exposition developed by Euclid in his famous book on Elements. The attitude of mathematicians towards this method has certainly evolved in the past centuries, but the relationship between understanding and acceptability of mathematical statements has not dramatically changed and still constitutes a characterising element of this discipline. This paper is aimed at explaining and discussing some aspects which may be considered at the origin of difficulties related to proof, in particular, it focusses on the tension between two poles, that of production and that of systematisation of mathematical knowledge.     

Suppression of pull-in instability in MEMS using a high-frequency actuation

We study the effect of a high-frequency AC tension on the pull-in instability induced by a DC tension in a microelectromechanical system. The microstructure is modelled as a single-degree-of-freedom system. The method of direct partition of motion is used to split the fast and slow dynamics. Analysis of steady-states of the slow dynamic enables us to depict the effect of the AC voltage on the pull-in. The main result of this paper indicates that it is possible to suppress the electrostatically induced pull-in instability for a range of values of the amplitude and the frequency of the high-frequency AC.     

Simulating the motion of the leech: A biomechanical application of DAEs

In this paper a mathematical model is developed for the dynamical behaviour of a hydrostatic skeleton. The basic configuration is taken from the worm-like shape of the medicinal leech. It consists of a sequence of hexahedra with damped elastic springs as edges to model the various parts of the musculature. The system is stabilized by the constraint of constant volume either in the whole body or in prescribed compartments. We set up Lagrange's equations of motion with the Lagrange multipliers being the pressure values in the compartments. The equations of motion lead to a large differential-algebraic system which is solved by an application of semi-explicit numerical methods. Though the model has not yet been adapted to experimental data, first simulations with a simplified set of parameters show that it is capable of generating basic movements of the leech such as crawling and swimming. This revised version was published online in June 2006 with corrections to the Cover Date.     

维纳和布朗运动

布朗运动,作为一种特殊的随机过程,在随机过程理论处于一个中心地位.布朗运动理论在其他许多领域也有重要应用.在布朗运动理论的发展和完善过程中,布朗,爱因斯坦和维纳等人都作出了重要贡献.通过解读原始文献,考察了维纳建立布朗运动数学理论的过程.揭示了维纳在布朗运动的数学理论严格化进程中的重要作用.