Suggestion for determining parameters in process with complex functional dependence in the area of production technologies

• Main Authors: Pejović Branko B., Mićić Vladan M., Todić Aleksandar T., Todić Tomislav N., Smiljanić Milenko R.
• Format: Article
• Language: English
• Published: Savez inženjera i tehničara Srbije 2014-01-01
• Series: Tehnika
• Subjects: complex functional relations; Taylor series; linear polynomials; multifactor orthogonal first order plan; statistic analysis; resistance of metals in hot plastic deformation
• Online Access: http://scindeks-clanci.ceon.rs/data/pdf/0040-2176/2014/0040-21761406985P.pdf

In this paper for complex processes in the field of production mechanical engineering, that describes with the product of step and exponential functions, unknown parameters are calculated. The starting complex function is reduced by suitable method to linear form and then using Taylor's formula developed in series surrounding center point of the experiment. Mathematical model obtained without factors interaction was compared with a similar regression functions. After some mathematical transformations this model allows to determination unknown parameters in the starting function. To simplify the experimental determination of the coefficients of regression and to simplify the analysis, linear model of first order with interactions in coded form was used. Transformation to natural coordinates is performed by using adequate equations. Verification of the suggested method was performed using characteristic experiment in the field of metal deformation. For well-known law of resistance of metals at hot plastic deformation, as a function of influencing factors, all unknown parameters were determined in two ways: by comparing corresponding linear functions and using available derived models. The regression function of prior thermo mechanical process technology was determined experimentally using orthogonal multiple factor first order plan. Also, required statistical analysis and testing of this model were performed. With graphical interpretation of obtained results in logarithmic coordinates, well fittings models and experimental results were shown. Finally, some possibilities for practical application of the proposed methods and models in the field of production engineering, especially in the case of complex processes, were suggested. This method, compared to other methods used for solving setting problem, is faster, more efficient and more reliable.