Jedynak R.,University of Technology and Humanities in Radom
Rheologica Acta | Year: 2015
The main purpose of this paper is to provide an easy-to-use approximation formula for the inverse Langevin function. The mathematical complexity of this function makes it unfeasible for an analytical manipulation and inconvenient for computer simulation. This situation has motivated a series of papers directed on its approximation. The best known solution is given by Cohen. It is used in a lot of statistically based models of rubber-like materials. The formula is derived from rounded Padé approximation [3/2]. The main idea of the presented approach in this paper relies on improvement of the precision of approximation formula for the inverse Langevin function by using multipoint Padé approximation method. We focused our study strongly on obtaining a simple and accurate approximation. It is assumed that the proposed approximation formula may be considered a useful tool for verification of the results obtained in other ways. Our results are supported by investigating several numerical examples. The paper also presents a few applications of computer software named Mathematica which can be used to calculate symbolically one point Padé approximants and numerically multipoint Padé approximants. Using this software, we showed also how to compute higher order derivatives of the inverse function in a simple and elegant way. This issue was discussed by Itskov et al. © 2014 The Author(s).
Wilczek A.,University of Technology and Humanities in Radom
Tribology International | Year: 2015
The aim of this paper is to study the influence of changes in the resistance of transducer connections of a thin-layer sensor on the accuracy of temperature measurement in the EHL contact. A model of the sensor was developed. The calculations were made for the assumed temperature distribution in the contact for two shape types of the transducer - symmetric and asymmetric. The results revealed the importance of a careful selection of transducer's dimensions and the need for the correction of measured temperatures in order to achieve higher measurement accuracy. The largest measurement deviation occurred in the area of maximum temperature. The distribution of temperatures obtained from the measurements with both symmetric and asymmetric transducers did not differ significantly. © 2015 Elsevier Ltd.
Puchalski A.,University of Technology and Humanities in Radom
Mechanical Systems and Signal Processing | Year: 2015
The method of utilising signals of vibration acceleration in the on-line and off-line diagnostics of mechanical defects of internal combustion engines is presented in the paper. The monitored vibration signals of the spark ignition (SI) engine in various maintenance states of the valve system were investigated. The suggested technique is based on mathematical methods of the lower triangular-orthogonal (LQ) factorisation and the singular value decomposition (SVD) of observation subspaces computed on a vibration time series after their angular resampling without any transformations in the frequency domain. The applied algorithm of data processing filters excessive information and allows the selection of diagnostic features (essential from the maintenance point of view) and generates the empirical model and matrix residuals assessed in the no-fault state as being 'zero'. Then, statistical feature vectors, for which the averaged successive singular values of the residuals of the observation subspaces of the vibration signals were assumed as components, were analysed. As a result of this procedure the vectors of lower dimensions reduced to components, allowing the classification of observations within all defined classes, were obtained. On the basis of these vectors a scalar measure - sensitive to the kind of defect - was proposed and verified. © 2014 Elsevier Ltd. All rights reserved.
Puchalski A.,University of Technology and Humanities in Radom
Journal of Vibroengineering | Year: 2014
In the era of embedded systems the qualifications of engines, machines and on-board vehicle devices into no-fault and fault categories on the basis of vibration signals is the process in conformity with the paradigm of pattern recognitions. The most popular way of looking for vibrodiagnostic features is based on frequency analysis and spectral properties of the observed signals. There is no doubt that the ‘a priori’ knowledge concerning objects being diagnosed is important in gathering information on technical states of mechatronic systems of vehicles. The diagnostic task of vehicle systems solved in the article was considered as the process realised according to properties of statistical signals originated from sensors of vibrations accelerations and not as searching for filtration algorithms of selective time-frequency properties. The data set originated from the observation of time series after angular resampling, without any transformations encompassing a frequency domain, was used in the selection procedure of diagnostic features. Orthogonal decompositions of subspace data matrices allowed to obtain the empirical model of the system. This fact was utilised for non parametric way of generating residual matrix, assessed in no-fault state as being ‘null’. The new non parametric way of diagnosing defects, on the basis of averaged first singular values of residuals determined for the investigated operation states, was also presented. The verified method allowed to perform the statistical analysis of the valve system of the SI engine, based on data originated from the single recording channel. © JVE INTERNATIONAL LTD. JOURNAL OF VIBROENGINEERING 2014.
Kowalska M.,University of Technology and Humanities in Radom
Journal of Dispersion Science and Technology | Year: 2016
The objective of the current study was to evaluate long-term stability of emulsions with rice oil by assessing their physical properties. For this purpose, six emulsions were prepared, their stability was examined empirically, and the most correctly formulated emulsion composition was determined using a computer simulation. Variable parameters (oil and thickener content) were indicated with optimization software based on Kleeman's method. Synthesized emulsions were studied by numerous techniques involving determination of particle size and distribution of emulsion, optical microscopy, viscosity, and novelty analysis—Turbiscan test. The emulsion containing 50 g of oil and 1.2 g of thickener had the highest stability. Empirically determined parameters proved to be consistent with the results obtained using the computer software. The computer simulation showed that the most stable emulsion should contain from 35.93 to 50 g of oil and 0.94 to 1.19 g of thickener. The computer software based on Kleeman's method proved to be useful for fast optimization of the composition and providing parameters of stable emulsion systems. Forming emulsions based on rice oil is a chance to introduce a new, interesting representative of functional food as well as a cosmetic product. © 2016, Copyright © Taylor & Francis Group, LLC.