The paper is intented to show a new, state space, discrete, non integer order model of a one-dimensional heat transfer process. The proposed model derives directly from time continuous, state space model and it uses the discrete Grünwald-Letnikov operator to express the fractional order difference with respect to time. Stability and spectrum decomposition for the proposed model are recalled, the accuracy and convergence are analyzed too. The convergence of the proposed model does not depend on parameters of heater and measuring sensors. The dimension of the model assuring stability and predefined rate of convergence and stability is estimated. Analytical results are confirmed by experiments.
The aim of the study was to analyse mechanical properties and microstructure of joints obtained using friction stir welding (FSW) technology. The focus of the study was on overlap linear FSW joints made of 1.4541 DIN 17441 steel sheets with thickness of 1.2 mm. Tools used during friction stir welding of steel joints were made of W-Re alloy. The joints were subjected to visual inspection and their load bearing capacity was evaluated by means of the tensile strength test with analysis of joint breaking mechanism. Furthermore, the joints were also tested during metallographic examinations. The analysis performed in the study revealed that all the samples of the FSW joints were broken outside the joint area in the base material of the upper sheet metal, which confirms its high tensile strength. Mean load capacity of the joints was 15.8 kN. Macroscopic and microscopic examinations of the joints did not reveal significant defects on the joint surface and in the cross-sections.