---

In this work, using finite element method (FEM) the effects of preload factor on the dynamic stability of noncircular two lobe hydrodynamic micropolar lubricated journal bearing based on the linear and nonlinear analytical dynamic models are presented. Assuming that the rotor is solid, the governing Reynolds equations for incompressible lubrication of journal bearing have been modified using micropolar theory. Later, the linear and nonlinear dynamic models, including a certain harmonic disturbances and time dependent trajectory of rotor center are applied to obtain the stability performance of bearing. The 4th order Rung-Kutta method has been used to solve the time dependent equations of rotor motion. Finally, the numerical results for the critical mass parameter and whirl frequency ratio of rotor as the stability characteristics of bearing are evaluated for different values of preload factor and compared together. Results show that the stability performance of two lobe bearing enhances by increasing the amount of bearing noncircularity in terms of the critical mass parameter increase and decrease of the whirl frequency ratio. Also, by comparing two dynamic analysis methods, it is obvious that the results of linear dynamic model are more cautious in different investigated cases. The results of nonlinear dynamic analysis reveal that by increasing the value of preload factor the dynamic response of rotor center involves return to steady state equilibrium position, limit cycle periodic motions and contact between rotor and bearing's shell.

---

Oil journal bearings are one of the most common parts of high load carrying rotating machine. Stability of these bearings can be affected by various stimulus such as changes in loading and lubrication conditions. Therefore, identification of the dynamic response of journal bearings can improve the control and fault detection process of rotor-bearings systems and prevent them from placing in critical operation condition. Since past, the mass unbalance of rotor is proposed as an effective factor on the dynamic behavior and long life of bearings. For this reason, in this research the effects of this parameter on the stability of hydrodynamic two lobe noncircular journal bearing with micropolar lubricant is investigated based on the nonlinear dynamic model. To achieve this goal, the governing Reynolds equation is modified with respect to micropolar fluid theory and the equations of rotor motion are derived considering the mass unbalance parameter. The static and dynamic pressure distributions of the lubricant film and the components of displacement, velocity and acceleration of the rotor are obtained by simultaneous solution of the Reynolds equation and the equations of rotor motion. Investigation of results in terms of dynamic trajectory, power spectrum, bifurcation diagram and Poincare map show that the dynamic behavior of two lobe bearings appears in different manner with variation of mass unbalance of rotor. The response of analyzed dynamic system include converge oscillations to the equilibrium point, periodic, KT periodic and quasi periodic behavior and also divergent disturbances which leads to collision between the rotor and bearing.

---

Today, oil journal bearings are widely used as an efficient support for rotary systems in various industries. When these bearings are used by loading in high speed conditions, whirling disturbances in the rotor motion status leading to collisions and abrasion is probable. Designing specific geometric shapes or applying industrial lubricants with different new combinations can affect the journal bearings ability to maintain their dynamic stability in critical situations. From this view, the use of non-circular bearings and non-Newtonian fluids in the field of lubrication has recently been heavily taken into consideration. In the present study by choosing non-Newtonian lubricant simulated by power law fluid model, the effects of design parameters such as eccentricity ratio, aspect ratio and power law index on dynamic stability of noncircular two, three and four lobe bearings are investigated. For this purpose, assuming the limited cycle oscillations of the rotor around the equilibrium point after damping the effects of initial imposed disturbances and using finite element numerical method to solve the governing equations, stability range of the system in form of linear dynamic analysis characteristics is determined based on the whirl frequency ratio and critical mass parameter. The results indicate that by increasing the power law index and decreasing aspect ratio, the dynamic range of bearing support will be developed. Also, by increasing the number of noncircular bearings lobes with power law lubricant and providing the system's positioning conditions in high values of eccentricity ratio, more ability to damping dynamic disturbances can be achieved.