This article shows the methodology of building finite element models of composite constructions made of laminate composites reinforced with carbon fibre fabric (carbon-fiber-reinforced polymer). The models use a repeatable microstructure of a composite -a repeated unit cell -which is a three-dimensional truss built with one-dimensional beam finite elements. Thanks to this fact, the models reflect the internal structure of the composite. The model constants have been experimentally determined. Therefore, the influence of production technology of the composite on its mechanical properties has been considered. The modelling methodology has been used to calculate deflections of exemplary composite constructions. The results have been experimentally verified.
Deflections of a thin cylindrical shell that is used in carding machines, either as a swift or a doffer, are analyzed in this paper. The shell may have supple supports at its edges and inner strengthening in the form of rings. The task of calculating the deflections has been solved by dividing the shell into longitudinal beam elements. The optimization procedure for criteria of mass minimum or deflection minimum is used. A numerical example to define selected construction data is presented along with the results.
Textile engineering processes require increased accuracy of the carding machines' working cylinders. In engineering calculations for designing the cylinders, the models should take into account flexibility and joint type. Moreover, the tolerances of manufacturing the component parts of the cylinders should be tighter. A continuous model and a discrete (finite element model) model that consider these factors of the working cylinder are presented in this paper. The results of the model analyses are compared with experimental measurements.Working cylinders (swifts and doffers) are important components of a carding machine. The quality of the web obtained in the carding process depends mainly on the accuracy of the shape of the surface, i.e., how much a real cylinder is different from a geometric one. Large differences between these two surfaces can cause a lack of uniformity or even break the web, which is the final product of carding.The real shape of the surface is influenced by deflection caused by reeling of the card clothing (elastic card clothing or metallic card wire) on the cylinder at tension.In the case where a metallic card wire is used in a worsted system, the pressure on the cylinder surface is the largest and the acceptable cylinder deflection is the smallest. Knowing the reeling force, it is possible to calculate the pressure on the cylinder surface:where S = reeling force, R = cylinder radius, and t = card clothing width.Working cylinders of modem carding machines are welded constructions, where the cylinder shell is wound from a steel sheet. To reduce the deflections caused by pressure po, the shell gauge of the cylinder must be appropriate. Similarly, thick shells are heavy and have a large mass moment of inertia, which causes problems in starting and stopping the machine. Therefore, the leading manufacturers of carding machines stiffen the cylinder shells from the inside using ring-like reinforcements (Figure 1 ).It is expected that the deflection under pressure po in a working cylinder will not exceed several hundredths of j ' 1 I FIGURE I. Working cylinder of carding machine. / a millimeter (typical size of a working cylinder is 0 = 1500 mm. L = 2500 mm, ~h = 15 mm). It is possible to estimate that, for pressures po in the real construction of cylinders, the reduced stress is small (on the order of a few MPa). Therefore, the main criterion used in engineering calculations is the deHection of a cylinder shell. Continuous Model of the CylinderIf we assume that the cylinder radius R and the shell gauge h are constant and all the joints of the constructional elements of the cylinder make the displacement of the joined surfaces impossible, the continuous model of the cylinder shown in Figure 2 may be used in deflection analysis.
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