An approximation of deflection line function at the rod loaded by buckling under self-weight

Rad se bavi aproksimacijom točne funkcije linije otklona za štap opterećen izvijanjem zbog vlastite težine pomoću funkcije, što je najbolje prikazano točnim oblikom ovog štapa. U ovom radu predlažemo metode derivacije kritične duljine izvijanja pomoću točnog rješenja i pomoću metode energije. Za zamjenske funkcije linije otklona su izabrane varijante goniometrijskih funkcija i polinomi. Pojedinačni koeficijenti funkcija su izabrani na temelju postojećih rubnih uvjeta i u slučaju nedovoljnog broja, oni su izabrani kako bi se izrazio točan oblik linije otklona štapa na najprikladniji način, koji je prenesen iz konkretnog primjera rješenja pomoću softvera SolidWorks. Rad prikazuje pogreške kritičnog izračuna duljine izvijanja nasuprot točnom rješenju, kao i maksimalna apsolutna i relativna odstupanja kod bočnog pomicanja za odabranu funkciju. Od pojedinačnih zamjenskih funkcija je naknadno izabrana ona koja ispunjava uvjet za opće korištenje i ima najmanja odstupanja od točnog rješenja.The paper deals with an approximation of the exact deflection line function at a rod loaded by self-weight buckling via the function, which is best-presented by the exact shape of this rod. In this paper, we suggest the methods of derivation of the critical buckling length by the exact solution and by the energy method. For the substitute functions of deflection line, the variants of goniometric functions and polynomials are chosen. Individual coefficients of the functions are chosen on the basis of existing boundary conditions and in the case of their insufficient count, they are chosen in order to express the exact rod deflection line shape in the most suitable way, which was transposed from the concrete example solution by SolidWorks Simulation software. The paper shows the errors of critical buckling length calculation against the exact solution, as well as the maximum absolute and relative deviations in the lateral displacement for the chosen function. From the individual substitute functions, one function that meets the condition for general use and has the lowest deviations from the exact solution, is subsequently chosen

Mathematical characterization of values of rheological variables during the networking reaction of rubber mixtures based on SBR

The article presents an analysis of cross-linking reaction using measurements of time dependencies of torque at constant temperature from the range 100 up to 200 degrees C. The measured results obtained on sample based on styrene - butadiene (SBS) prepared in the laboratory show the behaviour which can be well described by equations of chemical reactions of first-order kinetics. It is possible mathematically describe significant constants of the kinetics of networking reaction (induction period, reaction rate coefficient) by the solution of differential equations and by mathematical approximation. Constants are exponentially dependent on the temperature of vulcanization, while dependencies are Arrhenius like. Math description allows describe the progress of the vulcanization reaction also in the temperature range outside of the monitoring interval, i.e. in the area of extremely long times required for the realization of the cross-linking reaction

Monitoring of vulcanization process using measurement of electrical properties during linear increasing temperature

The article presents the possibilities of diagnostics of irreversible chemical reaction vulcanization in case of laboratory prepared rubber mixture based on styrene - butadiene (SBR) using measurements of selected physical parameters. Our work is focused on the measurement of current rheologic parameters (torque at defined shear deformation) and selected electrical parameters (DC conductivity) during linear increasing temperature. The individual steps of vulcanization are well identified by means of measurements of rheologic parameters, while significantly affecting the value of the electrical conductivity. The value of the electrical conductivity increases with the increasing of rate of the crossbridging reactions during vulcanization. The rate of the heating affects both types of measurements. When the rate of the heating is increasing the temperature of the beginning of networking step of reactions and also the rate of vulcanization grow. The sensitivity of the both types of measurements allows a good mathematical description of the temperature dependence of the torque and the electric conductivity during the vulcanization of rubber mixtures based on SBR

NEW POSSIBILITIES FOR INVESTIGATION OF THE TECHNOLOGICAL TEXTURE BASED ON MEASUREMENT OF ELECTRIC PARAMETERS: THEORETICAL ANALYSIS AND EXPERIMENTAL VERIFICATION

Texture is preferred orientation of crystallites in some polycrystalline materials. Different methods are applied to characterize the orientation patterns and determine the orientation distribution. Most of these methods rely on diffraction. This paper introduces the principle of a method used for characterization of ceramics texture based on anisotropy of electrical properties of crystallites in ceramics. The mathematical framework of this method is presented in theoretical part of our work. In experimental section we demonstrate how the theoretical result could be used to evaluate technology texture of ceramic material intended for the production of electronic insulators. K e y w o r d s

The Relationship Between Mechanical and Electrical Properties During Vulcanisation of SBR Based Rubber

The aim of this paper is description of vulcanization process by monitoring of selected electrical and mechanical parameters. The experiments have shown that the vulcanization process can be qualitatively and quantitatively evaluated on the basis of measurements of mechanical (standard procedure in rubber industry) and also electrical parameters. The results obtained for model system SBR rubber mixture under conditions of linear heating are presented also