Mathematical modeling of stability in rough elliptic bore misaligned journal bearing considering thermal and non-Newtonian effects

Abstract The paper briefly introduces a finite difference method based mathematical model to predict the stability of a finite journal bearing. The proposed method is used to integrate the geometrical irregularities of bearing such as non-circularity and surface roughness with the operational error like misalignment to represent more accurate film thickness. The bearing bore is assumed elliptic with longitudinal or transverse type wave pattern of roughness. A combined solution of Reynolds equation and Energy equation is made using effective influence Newton–Raphson method of error convergence. The non-Newtonian behavior of lubricant is addressed based on Power Law model. Thermal effect is considered adiabatic. Further to this analysis, the steady state and related perturbed pressures are estimated using linearization of bearing reaction. The dimensionless spring and damping coefficients are evaluated to find the critical mass and whirl ratio. Finally, the effect of misalignment bore ellipticity and roughness pattern on stability of such journal bearing is discussed in detail.