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.

This investigation deals with the vibration analysis of a rotating tapered shaft in Functionally Graded Material (FGM). The dynamic system is modeled using the Timoshenko beam theory (FSDBT) with consideration of gyroscopic effect and rotary inertia. The equations of motion are expressed by the hierarchical finite element method based on bi-articulated boundary conditions. The material properties are continuously varied in the thickness direction of a hollow shaft according to the exponential law function (E-FGM). The presented model is validated by comparing the numerical results found with the available literature. Various analyses are carried out to determine the influence of taper angle and material distribution of the two extreme materials on the dynamic behavior of FGM conical rotors system.

Centrifugal compressors have been used in many areas of the machinery. The centrifugal compressor design is very complex, and a unique design system needs to be developed. A centrifugal compressor design system should be easy to use in interface and also flexible for inputs and outputs. The design tool also needs to be able to predicate the compressor performance in a fairly accurate level. In this study, we have developed a general analyses and optimization approach in the design and performance analysis of centrifugal turbomachines. This approach is based on different methods starting from a 1D approach up to the 3D study of the internal flow. It presents itself as a robust procedure for predicting and understanding the phenomena associated with the operation of turbomachines, but also for predicting performance. Current design system includes initial parameter studies, throughflow calculation, impeller design. The main improvements of the design system are adding the interface to allow users easy to use, adding the input and output capabilities and modifying few correlations. Current design system can predict the blade loading and compressor performance better compared with original design system. To check the aerodynamic appearance of the centrifugal compressor impeller blades, we must change the impeller dimensions and focus on changing axial length, but when changing the blade numbers, the model that improved efficiency and power at the same time introduced a design with a 0.274% and 10.735% improvement in each respectively in comparison to the initial impeller at the design point.

The dynamic behavior of fluid film bearings is one of the principal factors, which affect the performance of the rotating machines. In this research, a rigid rotor supported by two identical hydrodynamic bearings is considered. The main objective of this work is to predict the influence of the damping film of the hydrodynamic bearings on the stability of the rotating machines. Analysis of variance requested to identify the frequency of a system by the effect of damping coefficients that affects the unbalance of the system investigated by employing two software is presented, Matlab to calculate damping and the frequency of the coefficients, the design of Experiments (DOE) for calculates statistical effect of these parameters on the frequency of the system. Thus, in the DOE two levels were use in fifteen factors resulting in forty-eight combinations according to the Plakett-Burman design. The effect and Pareto graphs have studied to identify which damping coefficients and diameters are responsible for producing greatly effects on frequency and stability. The results showed that the damping coefficient Czy and D10, D17 produce major effects, on the stability of the system.

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.