Abstract
In this paper, software, that allows studying the stress-strain state of the blade of a low-pressure hydraulic turbine, is being developed. A mathematical model according to which the blade, which is actually a hollow shell and is partially fixed, is replaced by a variable stiffness plate, representing in plan an annular sector with a pinched inner arc edge, is analyzed. In this paper, application software which enables the stress-strain analysis of various blades to be investigated using the Ritz variation method, depending on their geometrical and mechanical parameters as well as external loads, is being developed. The geometrical parameters of the blade are: inner and outer radii of the annular sector, annular sector angle, maximum blade thickness and relative thicknesses at different points. Mechanical parameters are the Young’s modulus and the Poisson's ratio of the material from which the blade is made, and the load is assumed to be evenly distributed. Since the thickness of the blade is variable, the input data is the relative thicknesses of the blade at different points. Bilinear interpolation and Lagrange polynomials of 9th degree are used to calculate the intermediate values. Based on the comparison of the results, the conclusion, that using bilinear interpolation is more expedient for calculating the value of sub-integral function, is made. The accuracy and temporal complexity of the numerical integration methods are analyzed, namely interpolation of the sub-integral function by a polynomial followed by analytical calculation and the use of a quadrature formula resulting from repeated integration using the Simpson’s rule. Based on the comparison of the results, the conclusion, that polynomial interpolation with the subsequent analytical solution is expedient, is made. The developed software package is used to calculate the stress-strain state of the plate that approximates the real LMZ blade (PL510). The results are compared with experimental data. Several blade configurations are also analyzed.
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