Rotating machines are very common in industry.To understand their behaviour is therefore,very important. When considering numerical analysis of such systems, their modelling needsto consider several important effects which are normally disregarded, such as damping and stiffness coefficients associated with the hydrodynamic interactions between the shaft and the supporting bearings. Hydrodynamic bearings play an important role in proper functioning of turbo machinery. They have a direct effect on the dynamic behaviour of this type of machine by adding stiffness to the system. In this paper harmonic analysis of the rotor is done to identify the frequency through the variation of the diameters by design of the optimization (DOE). In the DOE, two levels were used with a total of eleven diameters as parameters and four stiffness factors, which resuted in forty eight runs as per Plakett-Burman design (PBD) plan for answers. Pareto effect graphs and Main effects Plot have been studied to identify the influence of stiffness and the diameters responsible for producing major effects on frequency. We have seen that the stiffness Kyz and the diameters D4 and D10 have an effect on frequency. The results of the confirmatory tests showed that the Plackett-Burman method was very effective in optimizing of rotating machines.

The dynamic behavior of the rotors is influenced by the bearings mounted on them. The aim of this research is to study the effect of the stiffness, shaft diameters and dimensions of lubricated journal bearings on the stability of the system using DOE methodology. We first calculated the values of the real frequency and imaginary frequency of the rotor by the Matlab program, then we prepared a matrix containing forty eight tests according to the Placket Berman plan representing the number of experiments and nine columns representing the factors: the rotor diameters and the dimensions of the hydrodynamic bearing and the system stiffness, to find out the most factors affecting the frequency in The real part or the fictional part, and any of them, affects system stability. The results showed that the diameter D1 has the more significant positive effect on the real part frequency, compared to outer journal diameter Db that has a negative effect on the imaginary part frequency and vice versa, as affirmed by the plot of principal effects. By with this criterion one can estimate the frequency as well as the mode for which the system will become unstable. On the other hand, a finite element code has been written in MATLAB to know the eigenvalues, and critical velocity that correspond to the speed at which the unbalanced excitation coincides with the eigenvalue. The results of the tests showed that the finite element method (FEM) was very effective studying system stability.

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