Influence of micropolar parameters on the transient stability of lemon bore bearings

This study presents the steady-state and dynamic performance, along with a transient analysis, of lemon-bore noncircular journal bearings operating under a micropolar lubrication regime. The lubricant is treated as a micropolar fluid, which takes into account the effects of microstructures such as additives and contaminants. The modified Reynolds equation, attained based on the micropolar lubrication theory, is solved using the finite difference method on a 60 * 40 mesh grid. The dynamic stability is analysed through linearized rotor motion trajectories and the fourth-order Runge-Kutta method, incorporating initial disturbances. Results reveal that micropolar lubricants enhance load-carrying capacity by 15–25% compared to Newtonian fluids at eccentricity ratios (ε) of 0.25 and 0.35. Stability analysis demonstrates that increasing the coupling number <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mo stretchy="false">(</mml:mo> <mml:msup> <mml:mi>N</mml:mi> <mml:mn>2</mml:mn> </mml:msup> <mml:mo stretchy="false">)</mml:mo> </mml:math> , from 0.1 to 0.9 elevates the critical mass by 202% but reduces the stability margin. The results are validated with existing literature. The whirl frequency ratio decreases by 30–40% under micropolar lubrication, indicating superior damping. At critical mass <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mo stretchy="false">(</mml:mo> <mml:msub> <mml:mrow> <mml:mover> <mml:mi>M</mml:mi> <mml:mo stretchy="false">¯</mml:mo> </mml:mover> </mml:mrow> <mml:mi>J</mml:mi> </mml:msub> <mml:mo>=</mml:mo> <mml:msub> <mml:mrow> <mml:mover> <mml:mi>M</mml:mi> <mml:mo stretchy="false">¯</mml:mo> </mml:mover> </mml:mrow> <mml:mi>C</mml:mi> </mml:msub> <mml:mo stretchy="false">)</mml:mo> </mml:math> , trajectories converge to stable limit cycles, where the oscillation causes instability. This work especially combines lemon bore geometry with micropolar lubrication, which has been barely explored in previous studies. It studies, computationally, the ways micropolar parameters affect load capacity and stability across various eccentricities. This research provides a framework for optimizing high-speed rotor-bearing systems and advancing applications in turbomachinery and energy systems. The findings highlight the potential of tailored micropolar fluids to enhance bearing efficiency while mitigating instability in dynamic regimes.