تعيين سرعت هاي بحراني سيستم روتور به همراه ديسك پره دار هم ميزان و ناهم ميزان

چكيده انگليسي :

Determining Critical Speeds of Rotors with Tuned and Mistuned Bladed Disk Mohammad Shadmani m shadmani@me iut ac ir January 13 2018 Department of Mechanical Engineering Isfahan University of Technology Isfahan 84156 83111 IranDegree Master of Science Language PersianSupervisors Saeed Ziaei Rad Prof szrad@cc iut ac ir Reza Tikani Assist Prof r tikani@cc iut ac ir AbstractNowadays bladed disk rotors have many applications and they are noteworthy wherever turbines compressors aircraft engines fans etc are in service Critical speeds for a rotor are rotor spin speeds in which amplitudeof system may approach to infinity unless enough damping is provided When one or more critical speedsare to be traversed analyses are done that generally include computations to ensure that the machine is notinadvertently designed to run continuously at or near a critical speed Typically the cyclic symmetry assumptionis used to analyze the bladed disks but when the blades possess a slight dissimilarity in physical or structuralproperties this assumption is not correct and the system dynamics undergoes a dramatic change In this case the bladed disk is said to be mistuned This research has been designed to determine the critical speeds ofa bladed disk rotor system with tuned and mistuned blade arrays In order to do this first with the aid ofa distributed parameter model partial differential equations of motion were derived Two cases of modelingare considered one assuming the longitudinal transverse motion of the blades and the other one only assumingtransverse motion After the discretization of the equations proper transformations were applied to the matricesof the system to obtain time invariant matrices for both tuned and mistuned cases For the tuned case Colemantransformation is applied which transforms the coordinates to fixed frame coordinates called multi blade andresults in time invariant matrices but for the mistuned case even in spite of the use of Coleman transformation the matrices remain time dependent Thus further transformations are needed that are complex transformation permutation and modulation By means of these matrices modal analysis was performed on the bladed disk rotorto obtain the Campbell diagrams It was found that taking the longitudinal vibrations of the blades into accountcan drastically improve the evaluation of the rotor time response as well as computing the natural frequencies ofthe system An analysis on the forced vibration response was also performed through obtaining the frequencyresponse function for the disk center The results were compared for the tuned and mistuned system caseswhereas it was seen that there are more peaks in the frequency response function of mistuned system It showshigher probability of resonance because of mistuning which was previously reported in earlier researches Bycomparing the natural frequencies of tuned and mistuned systems additional frequencies were found due tothe presence detuning which were also seen previously After obtaining the Campbell diagrams a probabilisticanalysis was done on the natural frequencies and it became clear that the probability density function for themmay be considered as Gaussian with a good level of approximation and hence only two first statistical momentsare adequate to describe the statistical properties KeywordsRotordynamics Bladed disk Critical speed Mistuning Campbell diagram Monte Carlo method

شادماني، محمد

تعيين سرعت هاي بحراني سيستم روتور به همراه ديسك پره دار هم ميزان و ناهم ميزان

ديناميك روتور , ديسك پره دار , سرعت بحراني , ناهم ميزاني , نمودار كمبل , روش مونت كارلو