In this paper, steady-state and stability performance characteristics of circular and noncircular two-, three-, and four-lobe journal bearings with micropolar fluids are presented. For this purpose, lubricating oil containing additives and contaminants is modeled as micropolar fluid. The modified Reynolds equation in dynamical state is obtained using the micropolar lubrication theory, and it is solved by finite element method. The bearing performance characteristics in terms of load carrying capacity, whirl frequency ratio, and critical mass parameter of journal are determined for different values of design parameters such as eccentricity and aspect ratio, preload factor, and micropolarity characteristics of lubricant in terms of material characteristic length and coupling number. Results show that in the case of noncircular bearings, the critical mass to load carrying capacity ratio decreases with increasing of preload factor, so for a constant vertical external load, the stability performance of rotating system can be improved by replacing the circular journal bearing with similar noncircular types. The results compared with Newtonian fluids indicate that micropolar lubricant exhibits better steady-state and dynamic performance. Also, results reveal that upgrading the micropolarity characteristics of lubricant causes increase in critical mass, load carrying capacity but decrease in whirl frequency ratio. It is also observed that the effect of micropolar fluids is more pronounced at high coupling numbers.

In this work, the effects of preload factor on the stability performance of noncircular two and three lobe journal bearings with incompressible micropolar lubricant are presented based on the linear and nonlinear dynamic models. Assuming that the rotor is rigid, the governing Reynolds equation for the hydrodynamic lubrication of finite length lobed journal bearings has been modified using micropolar theory. Then, the linear and nonlinear dynamic models which include a certain harmonic disturbance and a time dependent trajectory of rotor center are applied to analyze the stability performance of the considered bearings. The generalized differential quadrature method and fourth-order Runge–Kutta technique have been used to solve the governing Reynolds equation and time-dependent dynamic equations of rotor motion, respectively. Finally, the numerical results for the critical mass parameter and the whirl frequency ratio of the rotor as the stability characteristics of the lobed bearings are obtained for different values of preload factor and are compared together. Results show that the dynamic stability of the noncircular bearings is enhanced by decreasing the preload factor i.e. increasing the amount of bearing noncircularity. These enhancements are in terms of increase of the critical mass parameter and decrease for the whirl frequency ratio. Also, by comparing the two dynamic analysis methods, it is seen that the results of linear model are more conservative in different investigated cases. The results of nonlinear analysis reveal that by changing the preload factor the dynamic responses of the lobed bearings appear in different manners. From the responses, it is observed that the type of dynamic trajectory of rotor center varies from stable fixed point to limit cycle periodic motions and also contact between rotor and bearing’s shell.

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In this research, the steady state and dynamic performances of two-lobe noncircular journal bearings with couple stress lubricant are presented. The lubricating oil, containing additives and contaminants, is modeled as the couple stress fluid. The modified Reynolds equation is obtained using the couple stress lubrication theory and is then solved by finite element method as an efficient numerical technique. The steady-state characteristics of bearings, including the load carrying capacity and attitude angle, are determined for various values of the couple stress parameter. The results show that applying the couple stress fluid improves the efficiency of two-lobe bearings in terms of an increased load carrying capacity and reduced attitude angle. Also, the stability performance of the investigated bearings is studied using rotor motion equations based on linear and nonlinear dynamic methods. The results indicate that any increase in the lubricant couple stress parameter enhances the bearing ability to damp the rotor perturbations. In other words, by varying the lubricant from Newtonian oil to the couple stress type and upgrading its properties, the curves of the critical mass parameter and whirl frequency ratio have an increasing and decreasing trend, respectively. Based on the fourth-order Runge–Kutta method results, the dynamic trajectory of the rotor center in the bearing space changes with increasing the couple stress parameter from diverging disturbances and limits the cycle perturbations around the bearing center to converging oscillations to the static equilibrium point. Moreover, the effect of changing lubricant properties on the two-lobe bearing’s performance is more pronounced at higher values of the couple stress parameter, especially with an increase in the noncircularity of bearings’ geometry.

Journal bearings are one of the most widely used types of supporting devices for industrial machinery, especially for high-speed rotary systems. Considering the importance of mechanical systems ability to control vibrations and motion disturbances, the design of noncircular journal bearings has been one of the appropriate techniques used in recent years. In the present work, the effects of mount angle as a noncircularity unique feature on the dynamic stability of lobed journal bearings with micropolar lubricant are studied. For this purpose, modified Reynolds equation based on the linear and nonlinear methods is solved by generalized differential quadrature (GDQ) method. Then the static and dynamic characteristics of two-, three- and four-lobe bearings including load carrying capacity, whirl frequency ratio, critical mass parameter and rotor perturbation in terms of bifurcation diagram and Poincare map are presented for different values of mount angle. Nonlinear analysis results indicate that variation of mount angle can change the rotor response from limit cycle oscillations to convergent perturbation to static equilibrium point. Further, against plain circular journal bearings, choosing an appropriate orientation or mounting angle provides the optimal stability of noncircular lobed journal bearings. Also, the linear analysis results for the range of dynamic stability are more cautious than the nonlinear method in most of investigated cases.