Stochastic Finite Element Method Of Static And Dynamic Characteristics For Turbine Blade

The uncertain parameters of blade which cannot be correctly measured or controlledin the design, manufacturing, installation and operation result in the randomness of thestatic and dynamic characteristics of the blade. In the traditional analysis method, it issupposed that the parameters of the blade are deterministic. It is difficult to explain whyit fails in normal operation even the blade is designed correctly by the traditionaldeterministic method. The stochastic finite element model of the static and dynamiccharacteristics for the turbine blade is presented in this thesis. It can solve theuncertainties of blade parameters and obtain the probabilistic characteristics of the staticand dynamic characteristics of the turbine blade. It is significant to study the static anddynamic random characteristics and has great values for the reliability design,manufacture and operation of the turbine blade.Based on the analyzing of characteristics of the design parameters of the blade, therotor speed is treated as a random variable, the Young's modulus and density of thematerial, the blade size, the damp and the restriction of the blade root are treated asrandom fields. The local averaging method is used for the discretization of random fieldin terms of high precision and rapid convergence. The stochastic Hamilton variationprinciple of the dynamic characteristics of blade is derived by the method of perturbationtechnique. The dynamic stochastic finite element equation of the blade is derived byusing the 20 node iso-parametric element, and the formulations of the mean and firstorder variation of the linear elastic stiffness matrix, the centrifugal force stiffness matrix,the mass matrix, the centrifugal force load vector, the steam pressure load vector areinduced. The stochastic potential energy principle of the static characteristics of blade isderived, and the static stochastic finite element equation of the blade is obtained. Themean and the first order variation expression of initial stress stiffness matrix for dynamicfrequency are obtained. A stochastic elastic restriction element is proposed to deal withthe variation of the elastic restriction of the blade roots. The formulations for the meanand first order variation of the stiffness matrix of the stochastic restriction element areobtained. The solution methods of the mean, sensitivity, variance and the coefficient ofvariation (COV) of the static response, natural frequency, mode and the steady dynamicresponse are presented in this thesis.Following the object-oriented finite element idea, a stochastic analysis program iscompiled. The static response, natural vibration characteristics and the steady dynamicresponse of a uniform straight blade with random parameters are analyzed. The results ofthe presedted method are in good coherence with those of the analytical approach and theMonte Carlo method.The static response, natural vibration characteristics and the steady dynamicresponse of a 432 blade with random parameters are analyzed, which is concluded that asmall variation of random parameters will induce a significant variation of the responsevariables.The stochastic finite element method can predict the means and variations of thestatic and dynamic characteristics and the sensitivities of the static and dynamiccharacteristics with respect to the random parameters. They are very important for thereliability design, the control of the dispersion degree of frequency and the adjusting ofthe frequency for the turbine blade.