Transient vibration phenomena in deep mine hoisting cables. Part 2: Numerical simulation of the dynamic response

A simulation model is presented which investigates the dynamic response of a deep mine hoisting cable system during a winding cycle. The response, namely the lateral motions of the catenary cable and the longitudinal motion of the vertical rope with conveyance is observed on the fast time scale, and the slow time scale is introduced to monitor the variation of slowly varying parameters of the system. The cable equivalent proportional damping parameters, and periodic excitation functions resulting from the cross-over cable motion on the winder drum are identified. Subsequently, the model is solved numerically using parameters of a double-drum multi-rope system. Since the system eigenvalues are widely spread and the problem is of stiff nature, the numerical simulation is conducted using a stiff solver. The results of the simulation demonstrate various transient non-linear resonance phenomena arising in the system during the wind. The nominal ascending cycle simulation results reveal adverse dynamic behaviour of the catenary largely due to the autoparametric interactions between the in- and out-of-plane modes. Principal parametric resonances of the lateral modes also occur, and conditions for autoparametric interactions between the lateral and longitudinal modes arise. Additionally, a transition through a number of primary longitudinal resonances takes place during the wind. The adverse dynamic motions in the system promote large oscillations in the cable tension which must be considered significant with respect to fatigue of the cable. It is noted that a small change in the winding velocity may cause large changes in the dynamic response due to the resonance region shifts. Consequently, the resonance modal interactions can be avoided, to a large extent, if the winding velocity is increased to an appropriate level.     

Unsteady three-dimensional model of electric arc. Part 1. Mathematical model and testing results

A non-stationary three-dimensional mathematical model of the electric arc of constant current in the approximation of a partial local thermodynamic equilibrium of plasma is presented. For the purpose of testing the model and computer code a computation of the isothermal laminar viscous fluid flow past a circular cylinder (the testing of the dynamic part of the system of equations) and a computation of the axisymmetric electric arc with a reduced anode attachment have been done. A fair agreement of numerical results with experimental data points overall to the correctness of the mathematical model and the numerical solution technique.     

Mathematical modeling of randomness and fuzziness phenomena in scientific studies: I. Mathematical and empirical foundations

The possibility theory as a mathematical model of randomness and fuzziness phenomena is considered in a variant that enables the modeling of both probabilistic randomness, including that inherent in unpredictably evolving stochastic objects whose probabilistic models cannot be empirically reconstructed and nonprobabilistic randomness (fuzziness) inherent in real physical, technical, and economical objects, human–machine and expert systems, etc. Some principal distinctions between the considered variant and the known possibility theory variants, in particular, in mathematical formalism and its relationship with probability theory, substantive interpretation, and applications exemplified by solving the problems of identification and estimation optimization, empirical reconstruction of a fuzzy model for a studied object, measurement data analysis and interpretation, etc. (in the paper “Mathematical Modeling of Randomness and Fuzziness Phenomena in Scientific Studies. II. Applications”) are shown.     

On critical phenomena in interacting growth systems. Part I: General

Components which are placed in a finite or infinite space have integer numbers as possible states. They interact in a discrete time in a local deterministic way, in addition to which all the components' states are incremented at every time step by independent identically distributed random variables. We assume that the deterministic interaction function is translation-invariant and monotonic and that its values are between the minimum and the maximum of its arguments. Theorems 1 and 2 (based on propositions which we give in a separate Part II), give sufficient conditions for a system to have an invariant distribution or a bounded mean. Other statements, proved herein, provide background for them by giving conditions when a system has no invariant distribution or the mean of its components' states tends to infinity. All our main results use one and the same geometrical criterion.     

On critical phenomena in interacting growth systems. Part II: Bounded growth

This paper completes the classification of some infinite and finite growth systems which was started in Part I. Components whose states are integer numbers interact in a local deterministic way, in addition to which every component's state grows by a positive integerk with a probability ^k (1-) at every moment of the discrete time. Proposition 1 says that in the infinite system which starts from the state all zeros, percentages of elements whose states exceed a given valuek0 never exceed (C) ^k , whereC=const. Proposition 2 refers to finite systems. It states that the same inequalities hold during a time which depends exponentially on the system size.     

Adaptive autoregressive modeling of non-stationary vibration signals under distinct gear states. Part 1: modeling

Non-parametric time-frequency techniques are increasingly developed and employed to process non-stationary vibration signals of rotating machinery in a great deal of condition monitoring literature. However, their capacity to reveal power variations in the time-frequency space as precisely as possible becomes a hard constraint when the aim is that of monitoring the occurrence of mechanical faults. Therefore, for an early diagnosis, it is imperative to utilize methods with high temporal resolution, aiming at detecting spectral variations occurring in a very short time. This paper proposes three new adaptive parametric models transformed from time-varying vector-autoregressive model with their parameters estimated by means of noise-adaptive Kalman filter, extended Kalman filter and modified extended Kalman filter, respectively, on the basis of different assumptions. The performance analysis of the proposed adaptive parametric models is demonstrated using numerically generated non-stationary test signals. The results suggest that the proposed models possess appealing advantages in processing non-stationary signals and thus are able to provide reliable time-frequency domain information for condition monitoring.     

Mathematical modeling of randomness and fuzziness phenomena in scientific studies. II. Applications

This paper considers some elements of the optimal fuzzy decision theory that are similar to the optimal statistical decision theory, in particular, the theory of optimal fuzzy identification and optimal fuzzy hypothesis testing, such as Neyman–Pearson statistical hypothesis testing and optimal fuzzy estimation along with a sequential fuzzy identification algorithm similar to the Wald sequential statistical criterion. Some elements of the fuzzy measuring and computing transducer theory and its applications in the problems of the analysis and interpretation of measurement experiment data are given.     

Oscillation phenomena in polyacetylene: R 1×S 1 Gross-Neveu model with a chemical potential

The phase structure of the two-dimensional Gross-Neveu model in a spacetime of the form R ¹×S ¹ and in the presence of a chemical potential μ is investigated. The phase portrait of the model is constructed in the parameter plane (μ, γ), where γ=1/L and L is the length of the circle S ¹. In the portrait there exist two massive phases, with spontaneously broken chiral invariance, as well as infinitely many massless symmetric phases. Such a vacuum structure leads to oscillations of the critical curve μ _c (γ) of chiral phase transitions. In addition, the particle number density in the vacuum state of the model oscillates if μ<μ _c (γl). Pis’ma Zh. éksp. Teor. Fiz. 68, No. 5, 431–436 (10 September 1998)     

The slowly reacting mode of combustion of gaseous mixtures in spherical vessels. Part 1: Transient analysis and explosion limits

Frank-Kamenetskii's analysis of thermal explosions is revisited, using also a single-reaction model with an Arrhenius rate having a large activation energy, to describe the transient combustion of initially cold gaseous mixtures enclosed in a spherical vessel with a constant wall temperature. The analysis shows two modes of combustion. There is a flameless slowly reacting mode for low wall temperatures or small vessel sizes, when the temperature rise resulting from the heat released by the reaction is kept small by the heat-conduction losses to the wall, so as not to change significantly the order of magnitude of the reaction rate. In the other mode, the slow reaction rates occur only in an initial ignition stage, which ends abruptly when very large reaction rates cause a temperature runaway, or thermal explosion, at a well-defined ignition time and location, thereby triggering a flame that propagates across the vessel to consume the reactant rapidly. Explosion limits are defined, in agreement with Frank-Kamenetskii's analysis, by the limiting conditions for existence of the slowly reacting mode of combustion. In this mode, a quasi-steady temperature distribution is established after a transient reaction stage with small reactant consumption. Most of the reactant is burnt, with nearly uniform mass fraction, in a subsequent long stage during which the temperature follows a quasi-steady balance between the rates of heat conduction to the wall and of chemical heat release. The changes in the explosion limits caused by the enhanced heat-transfer rates associated with buoyant motion are described in an accompanying paper.     

Numerical modelling of unsteady heating and melting of the anode by electric arc. Part 1. Mathematical model and computed characteristics of the arc column

The two-dimensional mathematical model in the approximation of a partial local thermodynamic equilibrium of plasma and the technique for numerical computation of the unsteady electric arc characteristics, including the conjugate heat exchange of the electric-arc plasma flow with the treated product (anode) are considered. The results of overall testing of the numerical algorithm point to the correctness of the model and computational technique. The results of the computation of the arc characteristics from the conventional ignition moment until the passage to stationary regime are presented. It is found that a single thermal torus, which scatters fairly quickly in the ambient medium, forms around the arc column.