Nonlinear analysis of rotor-stator dynamic system with gear transmission under water lubrication bearing

This study presents a comprehensive nonlinear dynamic analysis of a water-lubricated bearing–gear–rotor system by incorporating the effects of turbulent mixed lubrication and system damping. A dimensionless model was developed and numerically solved using the fourth-order Runge–Kutta method. The dynamic responses under various dimensionless rotational speed ratios ( s ) and damping ratios ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mi>ξ</mml:mi> </mml:mrow> </mml:math> ) were systematically investigated through bifurcation diagrams, dynamic orbits, Poincaré maps, power spectra, fractal dimension, and Lyapunov exponent analysis. The results reveal that the system exhibits chaotic behavior at low speed ratios ( s&lt;1.2 ) and low damping values ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mi>ξ</mml:mi> <mml:mo>&lt;</mml:mo> <mml:mn>0.14</mml:mn> </mml:mrow> </mml:math> ), characterized by non-periodic motion, scattered Poincaré return points, and a broad excitation spectrum. As speed or damping increases, the system transitions into periodic states, though intermittent chaos reappears within specific damping intervals. At <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mi>ξ</mml:mi> <mml:mo>=</mml:mo> <mml:mn>0.1</mml:mn> <mml:mo>,</mml:mo> </mml:mrow> </mml:math> all components, that is, bearing, gear, and rotor, demonstrated chaotic dynamics, as confirmed by non-integer fractal dimensions ( 2.05, 1.60, and 1.97 ) and positive Lyapunov exponents ( 0.22, 0.12, and 0.16 ). These findings highlight the complex influence of speed and damping on the stability and performance of water-lubricated systems. The results provide valuable insights for the design and control of high-performance, low-viscosity fluid-lubricated machinery operating under nonlinear and potentially chaotic conditions.