A comparative study of the preload effects on the stability performance of noncircular journal bearings using linear and nonlinear dynamic approaches

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.