The Determination of the Dependency between the Input and Output Parameters in Fused Deposition Modeling (FDM) Using Multi Polytropic Functions

In the process of determination of the input-output correlations for FDM technology, researchers usually consider polynomial or simple polytropic functions. For these functions the method of least squares leads to linear systems from which the unknowns are easily determined. The approximations given by polynomial and polytropic functions do not offer the possibility for the extrapolation of the results for other intermediate or extrapolated points, or the obtained results are very different comparing to the experimental ones. For these reasons in this paper we purpose the use of the multi polytropic functions, in which the polytropic exponents have real non-zero values. The obtained system from which the polytropic coefficients and exponents is no longer a linear one. Because of the convergence conditions of the Newton-Raphson method, this method is not a valid one for the solving of this system in the general case. The solving of the system is performed with the aid of the gradient method. An example highlights the theory.