Investigation On Dynamic Properties Of Rotor System With Uncertain Parameters Based On Interval Analysis Method

For many years, research mainly focuses on vibration analysis for deterministic rotor systems, which means the analysis and design base on deterministic structure parameters and model. There are few discussions on changes of the rotor system’s dynamic characteristics with uncertain structure parameters. In fact, structure parameters of the rotor system are inevitably changing within certain range due to changes of material/geometry properties, machining error and temperature. Research on dynamic characteristics of the rotor system with uncertain parameters is then obviously important as it provides theory fundament for the design of aeroengines.In this thesis, the critical speed and unbalanced responses of the rotor system with uncertain parameters are studied using interval analysis method. Additionally studies on reliability assessment method are carried based on non-probabilistic robust reliability analysis theory. Main content of this thesis are as following:Interval theory is introduced firstly as the theory fundament of the whole thesis. Comparing analysis are carried for Dief method, interval perturbation method, Qiu method and subinterval perturbation method through which ap plication scope and advantages and disadvantages are given for each method. With basic theorems of matrix analysis, matrix inequality algorithm is brought up for interval matrix eigenvalue problem.Non-probabilistic interval analysis method is raised to study the critical speed of the rotor system with uncertain parameters. Based on interval mathematics and interval perturbation theory, the algorithm of natural frequencies is raised. Then the relationship of natural frequencies changing with varying system parameters and the scope of the critical speed are obtained.Unbalance responses of the rotor system with uncertain parameters are studied. Based on Taylor series expansion and interval extension theory, interval analysis method is introduce to estimate the interval of unbalance responses by qualifying uncertain parameters of the rotor system with interval vectors.Non-probabilistic robust reliability criterion raised by Ben-haim is improved according to set theory and interval mathematics before being appl ied in the analysis of the rotor system. Structure natural frequencies are given through interval parameter perturbation method. Before analyzing the rotor system’s nonprobabilistic reliability, the robust reliability indexes for vibration of rotor are defined.Modal interval analysis(MIA) which defers classic interval analysis(CIA) is introduced. Given the basic theory of modal interval analysis, the application in dynamic eigenvalues problem of systems with uncertain parameters is discussed. Based modal interval analysis, a new method for obtaining the natual frequencies of the rotor system with uncertain parameters is raised.