Faculty of Mechanical and Civil Engineering, Kraljevo

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Energy and exergy analysis of biomass gasification at different temperatures
(2010) Karamarkovic, Rade; Karamarkovic V.
Biomass is usually gasified above the optimal temperature at the carbon-boundary point, due to the use of different types of gasifiers, gasifying media, clinkering/slagging of bed material, tar cracking, etc. This paper is focused on air gasification of biomass with different moisture at different gasification temperatures. A chemical equilibrium model is developed and analyses are carried out at pressures of 1 and 10 bar with the typical biomass feed represented by CH1.4O0.59N0.0017. At the temperature range 900-1373 K, the increase of moisture in biomass leads to the decrease of efficiencies for the examined processes. The moisture content of biomass may be designated as optimal only if the gasification temperature is equal to the carbon-boundary temperature for biomass with that specific moisture content. Compared with the efficiencies based on chemical energy and exergy, biomass feedstock drying with the product gas sensible heat is less beneficial for the efficiency based on total exergy. The gasification process at a given gasification temperature can be improved by the use of dry biomass and by the carbon-boundary temperature approaching the required temperature with the change of gasification pressure or with the addition of heat in the process. © 2009 Elsevier Ltd. All rights reserved.
On the instability of equilibrium of nonholonomic systems with nonhomogeneous constraints
(2010) Čović V.; Vesković, Miroslav; Obradovic, Aleksandar
The first Lyapunov method, extended by V. Kozlov to nonlinear mechanical systems, is applied to the study of the instability of the equilibrium position of a mechanical system moving in the field of potential and dissipative forces. The motion of the system is subject to the action of the ideal linear nonholonomic nonhomogeneous constraints. Five theorems on the instability of the equilibrium position of the above mentioned system are formulated. The theorem formulated in [V.V. Kozlov, On the asymptotic motions of systems with dissipation, J. Appl. Math. Mech. 58 (5) (1994) 787-792], which refers to the instability of the equilibrium position of the holonomic scleronomic mechanical system in the field of potential and dissipative forces, is generalized to the case of nonholonomic systems with linear nonhomogeneous constraints. In other theorems the algebraic criteria of the Kozlov type are transformed into a group of equations required only to have real solutions. The existence of such solutions enables the fulfillment of all conditions related to the initial algebraic criteria. Lastly, a theorem on instability has also been formulated in the case where the matrix of the dissipative function coefficients is singular in the equilibrium position. The results are illustrated by an example. © 2009 Elsevier Ltd. All rights reserved.
Brachistochronic motion of a nonholonomic rheonomic mechanical system
(2010) Obradovic, Aleksandar; Čović V.; Vesković, Miroslav; Drazic M.
The brachistochrone problem of the rheonomic mechanical system whose motion is subject to nonholonomic constraints is solved with nonlinear differential equations of motion. Apart from control forces, the system is influenced by the action of other known potential and nonpotential forces as well. The problem of optimal control is solved by applying Pontryagin's Maximum Principle and the singular optimal control theory. This procedure results in the two-point boundary value problem for the system of ordinary nonlinear differential equations of the first order, with a corresponding number of initial and end conditions. This paper determines the control forces that are realized by imposing on the system a corresponding number of independent ideal holonomic constraints, without the action of active control forces. These constraints must be in accordance with the previously determined brachistochronic motion. The method is illustrated with a single complex example that represents the first known concrete demonstration of brachistochronic motion of the nonholonomic rheonomic mechanical system. © 2010 Springer-Verlag.
On the stability of equilibria of nonholonomic systems with nonlinear constraints
(2010) Čović V.; Vesković, Miroslav; Djuric D.; Obradovic, Aleksandar
Lyapunov's first method, extended by V. V. Kozlov to nonlinear mechanical systems, is applied to the study of the instability of the position of equilibrium of a mechanical system moving in the field of conservative and dissipative forces. The motion of the system is limited by ideal nonlinear nonholonomic constraints. Five cases determined by the relationship between the degree of the first nontrivial polynomials in Maclaurin's series for the potential energy and the functions that can be generated from the equations of nonlinear nonholonomic constraints are analyzed. In the three cases, the theorem on the instability of the position of equilibrium of nonholonomic systems with linear homogeneous constraints (V. V. Kozlov (1986)) is generalized to the case of nonlinear nonhomogeneous constraints. In the other two cases, new theorems are set extending the result from V. V. Kozlov (1994) to nonholonomic systems with nonlinear constraints. © Shanghai University and Springer-Verlag Berlin Heidelberg 2010.
Analytical solution for the problem of maximum exit velocity under Coulomb friction in gravity flow discharge chutes
(2010) Šalinić, Slaviša
In this paper, an analytical solution for the problem of finding profiles of gravity flow discharge chutes required to achieve maximum exit velocity under Coulomb friction is obtained by application of variational calculus. Themodel of a particle whichmoves down a rough curve in a uniform gravitational field is used to obtain a solution of the problem for various boundary conditions. The projection sign of the normal reaction force of the rough curve onto the normal to the curve and the restriction requiring that the tangential acceleration be non-negative are introduced as the additional constraints in the form of inequalities. These inequalities are transformed into equalities by introducing new state variables. Although this is fundamentally a constrained variational problem, by further introducing a new functional with an expanded set of unknown functions, it is transformed into an unconstrained problem where broken extremals appear. The obtained equations of the chute profiles contain a certain number of unknown constants which are determined from a corresponding system of nonlinear algebraic equations. The obtained results are compared with the known results from the literature. © 2010 Springer-Verlag.
Robust identification of pneumatic servo actuators in the real situations
(2011) Filipovic, Vojislav; Nedić, Novak; Stojanović, Vladimir
Intensive research in the field of mathematical modelling of the pneumatic cylinder has shown that its mathematical model is nonlinear and that a lot of important details cannot be included in the model. Selection of the model and the identification method have been conditioned by the following facts: (a) The nonlinear model of the system can be approximated by a linear model with time-variant parameters. (b) There is the influence of the combination of heat coefficient, unknown discharge coefficient and change of temperature on the pneumatic cylinder model. Therefore it is assumed that the parameters of the pneumatic cylinder are random (stochastic parameters). (c) In practical conditions, observations have a non-Gaussian distribution. Due to the abovementioned reasons, it is assumed that the pneumatic cylinder model is a linear stochastic model with variable parameters. The Masreliez-Martin filter (robust Kalman filter) was used for identification of parameters of the model. For the purpose of increasing the practical value of the filter, the following two heuristic modifications were performed: (1) It was adopted that T (k) = 1 holds for the scalar transformation of residuals. (2) Fisher information was approximated by a derivative of the Huber's function. The proposed modifications were confirmed through intensive simulations. In order to provide persistent excitation, the autocovariance function 1/f of the signal was used. The behaviour of the new approach to identification of the pneumatic cylinder is illustrated by simulations. © Springer-Verlag 2011.
Optimization of a pentagonal cross section of the truck crane boom using Lagrange's multipliers and differential evolution algorithm
(2011) Gašić, Milomir; Savković, Mile; Bulatovic, Radovan; Petrovic R.
The cross sections of truck crane booms are complex box-like cross sections which should provide continuous stress distribution. It is difficult to analytically determine the optimal relations among geometric parameters of such cross sections. The paper deals with the method for determination of relations among geometric parameters in order to reach the optimal shape of the cross section. The method is based on Lagrange's multipliers used for determination of extreme values. The optimization of geometric parameters has been also done by the algorithm of Differential Evolution (DE). The optimization of cross section is based on the strength criterion. The results of applied methods have been verified by means of numerical example for an existing solution. The comparative analysis of the results of both methods has been done, too. © 2010 Springer Science+Business Media B.V.
Analysis of the axle fracture of the bucket wheel excavator
(2011) Savković, Mile; Gašić, Milomir; Arsić M.; Petrovic R.
The common design of the bucket wheel drive mechanism in some bucket wheel excavators (BWE) consists of a gearbox and a hollow shaft, while the bucket wheel is supported by the axle passing through the hollow shaft. Improper maintenance and inadequate elimination of axis misalignment of the hollow shaft and the bucket wheel axle are the main causes of excavator failure and axle fracture. The paper examines the causes of bucket wheel axle fractures.Experimental testing of the chemical composition and mechanical properties of the material used to make the bucket wheel axle and metallographic inspections of the fracture surfaces in the bucket wheel axle by means of electronic and light microscope carried out in the first part of the paper have shown that there are no significant inhomogeneities and errors in the material of the axle.The second part of the paper presents the FEM analysis of influences of disturbances on the manner of support of the bucket wheel axle on the fracture. It shows that the negative influences of support of the axle reflected through the increase in the stress concentration and occurence of the initial crack are the main causes of the axle fracture. © 2010 Elsevier Ltd.
Design of constant gain controllers for the hydraulic control system with a long transmission line
(2011) Nedić, Novak; Dubonjic, Ljubisa; Filipovic, Vojislav
The paper presents the problems of describing the system of a pump-controlled motor with a long transmission line by means of a mathematical model with lumped parameters where the long transmission line is divided into n segments. The mathematical model thus obtained is of high order but its order is reduced by applying the appropriate methodology, which considerably increases its use value. A P controller was designed for that mathematical model of the system. The graphical method which includes performances (specification of damping of the system) and stability margins was used in the design. Thanks to strong software support, the complexity of synthesis of controllers was considerably reduced in comparison with the methods presented in the literature. Dynamic behavior of the closed loop system was treated in intensive simulation. The methodology applied provides significant energy savings. © Springer-Verlag 2011.
Global exponential stability of switched systems
(2011) Filipovic, Vojislav
This paper proposes a method for the stability analysis of deterministic switched systems. Two motivational examples are introduced (nonholonomic system and constrained pendulum). The finite collection of models consists of nonlinear models, and a switching sequence is arbitrary. It is supposed that there is no jump in the state at switching instants, and there is no Zeno behavior, i.e., there is a finite number of switches on every bounded interval. For the analysis of deterministic switched systems, the multiple Lyapunov functions are used, and the global exponential stability is proved. The exponentially stable equilibrium of systems is relevant for practice because such systems are robust to perturbations. © 2011 Shanghai University and Springer-Verlag Berlin Heidelberg.
Control of the optimum synthesis process of a four-bar linkage whose point on the working member generates the given path
(2011) Bulatovic, Radovan; Dorević S.
This paper presents the optimum synthesis of a four-bar linkage in which the coupler point performs a path composed of rectilinear segments and a circular arc. The Grashof four-bar linkage whose geometry provides minimum deviations from the given problem for certain parts of the crank cycle is chosen. The motion of the coupler point of the four-bar linkage is controlled within the given values of allowed deviations so that it is always in the prescribed environment of the given point on the observed segment. The synthesis process tends to bring only those path segments that are beyond the boundaries within the prescribed boundary deviations. During the synthesis, allowed deviations change from the initial maximum values to the given minimum ones. Groups of mechanisms realising satisfactory approximation to the desired motion can be obtained by the method of controlled decrease of allowed deviations with the application of the Differential Evolution (DE) algorithm. © 2011 Elsevier Inc. All rights reserved.
Determination of joint reaction forces in a symbolic form in rigid multibody systems
(2011) Šalinić, Slaviša
This paper presents an algorithm for determination of joint reaction forces in a symbolic form in planar and spatial tree structure rigid multibody systems. The frictionless revolute and prismatic joints are taken into consideration. The algorithm is based on the use of Kane's equations with undetermined multipliers of constraints. The expressions for the reaction forces and the torques of reaction couples in the joints are obtained in a form that does not require matrix inversion and allows an easy and straightforward implementation in programming environments for symbolic computations (like Mathematica, Maple etc.). The application of the proposed algorithm to the problem of determination of static friction forces in locked Coulomb friction joints is indicated. The algorithm has been illustrated by using both a gymnast on a trampoline and a Puma manipulator. © 2011 Elsevier Ltd.
Optimization of trapezoidal cross section of the truck crane boom by lagrange's multipliers and by differential evolution algorithm (DE)
(2011) Gašić, Milomir; Savković, Mile; Bulatovic, Radovan
The cross sections of truck crane booms are complex box-like cross sections, which should provide continuous stress allocation. It is difficult to analytically determine optimal relations among geometric parameters of such cross sections. The paper deals with the method for determining relations among geometric parameters in order to achieve the optimal shape of the cross section. The method is based on Lagrange's multipliers used for determination of extreme values. The optimisation of geometric parameters has also been done with the method of differential evolution (DE). The optimisation of the cross section is based on the strength criterion. The results of the applied methods have been verified by means of numerical example for an existing solution. The comparative analysis of the results of both methods has also been done. © 2011 Journal of Mechanical Engineering. All rights reserved.
Lyapunov-Kozlov method for singular cases
(2011) Čović V.; Djuric D.; Vesković, Miroslav; Obradovic, Aleksandar
Lyapunov's first method, extended by Kozlov to nonlinear mechanical systems, is applied to study the instability of the equilibrium position of a mechanical system moving in the field of conservative and dissipative forces. The cases with a tensor of inertia or a matrix of coefficients of the Rayleigh dissipative function are analyzed singularly in the equilibrium position. This fact renders the impossible application of Lyapunov's approach in the analysis of the stability because, in the equilibrium position, the conditions of the existence and uniqueness of the solutions to the differential equations of motion are not fulfilled. It is shown that Kozlov's generalization of Lyapunov's first method can also be applied in the mentioned cases on the conditions that, besides the known algebraic expression, more are fulfilled. Three theorems on the instability of the equilibrium position are formulated. The results are illustrated by an example. © 2011 Shanghai University and Springer-Verlag Berlin Heidelberg.
Remarks on Cone metric spaces and fixed point theorems of T-Kannan and T-Chatterjea contractive mappings
(2011) Filipović M.; Paunović L.; Radenovíc S.; Rajović, Miloje D.
Recently, José R. Morales and Edixon Rojas [José R. Morales and Edixon Rojas, Cone metric spaces and fixed point theorems of T-Kannan contractive mappings, Int. J. Math. Anal. 4 (4) (2010) 175-184] proved fixed point theorems for T-Kannan and T-Chatterjea contractions in cone metric spaces when the underlying cone is normal. The aim of this paper is to prove this without using the normality condition. Two results for these classes of contractive mappings are also proved. Examples are given to illustrate the results. © 2011 Elsevier Ltd.
Instability of equilibrium of nonholonomic systems with dissipation and circulatory forces
(2011) Vesković, Miroslav; Čović V.; Obradovic, Aleksandar
The paper discusses the equilibrium instability problem of the scleronomic nonholonomic systems acted upon by dissipative, conservative, and circulatory forces. The method is based on the existence of solutions to the differential equations of the motion which asymptotically tends to the equilibrium state of the system as t tends to negative infinity. It is assumed that the kinetic energy, the Rayleigh dissipation function, and the positional forces in the neighborhood of the equilibrium position are infinitely differentiable functions. The results obtained here are partially generalized the results obtained by Kozlov et al. (Kozlov, V. V. The asymptotic motions of systems with dissipation. Journal of Applied Mathematics and Mechanics, 58(5), 787-792 (1994). Merkin, D. R. Introduction to the Theory of the Stability of Motion (in Russian), Nauka, Moscow (1987). Thomson, W. and Tait, P. Treatise on Natural Philosophy, Part I, Cambridge University Press, Cambridge (1879)). The results are illustrated by an example. © 2011 Shanghai University and Springer-Verlag Berlin Heidelberg.
On the brachistochrone of a variable mass particle in general force fields
(2011) Jeremić O.; Šalinić, Slaviša; Obradovic, Aleksandar; Mitrović Z.
The problem of the brachistochronic motion of a variable mass particle is considered. The particle moves through a resistant medium in the field of arbitrary active forces. Beginning from these general assumptions, and applying Pontryagin's minimum principle along with singular optimal control theory, a corresponding two-point boundary value problem is obtained and solved. The solution proposed involves an appropriate numerical procedure based upon the shooting method. In this numerical procedure, the evaluation of ranges for unknown values of costate variables is avoided by the choice of a corresponding Cartesian coordinate of the particle as an independent variable. A numerical example assuming the resistance force proportional to the square of the particle speed is presented. A review of existing results for related problems is provided, and it can be shown that these problems may be regarded as special cases of the brachistochrone problem formulated and solved in this paper under very general assumptions by means of optimal control theory. © 2011 Elsevier Ltd.
Thermal memory influence on the thermoconducting component of indirect photoacoustic response
(2012) Nesic, Mioljub; Gusavac P.; Popović, Marica; Šoškić, Zlatan; Galovic, Slobodanka
In this paper, a model of the thermoconducting component of the indirect photoacoustic (PA) response is derived that includes thermal memory properties of the examined material and its fluid environment. A comparison is made between the derived model and the classic one, which neglects the influence of thermal memory. It has been shown that, at modulation frequencies lower than a certain boundary frequency of the light source, these models tend to overlap, while at higher frequencies, noticeable differences occur. The boundary frequency depends on heat propagation velocity through the sample and its thickness. This observation limits the validity domain of previous models to a range lower than the boundary frequency, offering, at the same time, the possibility of obtaining thermal memory properties using PA effects at frequencies above it. © 2012 The Royal Swedish Academy of Sciences.
Characterization of alloys and liquidus projections of ternary Bi-Sb-Sn system
(2012) Minic D.; Kolarevic, Milan; Manasijevic D.; Ćosović V.; Živković D.; Talijan N.; Markovic M.
Given that Sn-based lead-free solders are considered as possible substitution for standard lead-tin solders, properties of the alloys from ternary Bi-Sb-Sn system were characterized by microstructural SEM-EDS analysis, Brinell hardness tests, and electrical conductivity measurements. Isothermal cross section at 298 K and liquidus surface projection were calculated by application of CALPHAD method and software package PANDAT 8.1. The experimentally determined phase compositions in analyzed microstructures were found to be in a good agreement with phases on calculated cross sections. Copyright © 2012 De Gruyter.
Photothermal thermoelastic bending for media with thermal memory
(2012) Nesic, Mioljub; Galovic, Slobodanka; Šoškić, Zlatan; Popović, Marica; Jakovcev-Todorovic D.
Photothermal thermoelastic bending depends on an optically generated dynamic thermal field distribution within a sample. A generalized description of the distribution is proposed, including the effects of a finite heat propagation velocity and a finite, non-zero time of thermal relaxation (known as thermal memory effects in generalized heat conduction theory), and finally the generated thermoelastic bending is calculated by using both a thin solid-plate approximation and a decoupling system of thermoelastic equations. The comparison between this model and the classical one, which does not account for thermal memory influence, has been made. If the sample is thicker than the value of its minimal thermal diffusion length, the difference between the two models becomes insignificant. Otherwise, it has been shown that the two models tend to overlap at low and high modulation frequencies of the excitation light, while in the mid-frequency range, some deviations become more apparent and thermal memory properties of the sample must be taken into account. The suggested model enables evaluation of thermal memory properties for such a solid. © 2012 Springer Science+Business Media, LLC.

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