Bifurcation and Chaos of Gear/Pinion Transmission System Supported by Journal Bearings with Temperature Effect

IntroductionThe gear-bearing system plays a critical role in turbo-machinery. Nonlinear dynamics of the system, particularly the suspension effects, gear mesh forces, and temperature-dependent viscosity, significantly influence its performance. Understanding the system's behavior, especially under varying rotational speeds and temperatures, is essential to avoid catastrophic failures. This study investigates the nonlinear dynamic behavior of a pinion/gear system under such conditions.PurposeThe purpose of this study is to systematically analyze the nonlinear dynamic behavior of a gear-bearing system, considering the effects of nonlinear suspension, nonlinear oil-film forces, nonlinear gear mesh forces, and temperature-dependent viscosity. The study aims to identify chaotic motions and other dynamic behaviors under various operational conditions.MethodsThe nonlinear dynamic equations governing the system are solved using the fourth-order Runge-Kutta method, with a time step of pi/300 and a convergence criterion of less than 0.0001. Several analytical tools, including bifurcation diagrams, dynamic trajectories, Poincar & eacute; maps, Lyapunov exponents, and fractal dimensions, are used to analyze the system's behavior. The bifurcation control parameters include the dimensionless rotational speed ratio, unbalance parameter, and damping ratio, with a focus on different temperatures (T = 25 degrees C, 40 degrees C, 50 degrees C, and 80 degrees C).ResultsThe study finds a wide range of dynamic behaviors, including periodic, sub-harmonic, and chaotic motions. The bifurcation diagrams indicate transitions from irregular to regular motions at various rotational speeds, with non-periodic motions observed at higher speeds. The Poincar & eacute; maps and Lyapunov exponents confirm the onset of chaotic behavior, particularly at certain rotational speeds and temperatures. The dynamic responses of the gear and bearing geometric centers are often non-synchronous, with synchronization occurring at specific points. Temperature increases result in the degradation of lubrication and larger vibration amplitudes, especially at high speeds.DiscussionThe findings highlight the importance of considering temperature-dependent viscosity in dynamic analyses. Neglecting temperature effects, particularly at low rotational speeds, can significantly underestimate the system's dynamic behavior. The non-synchronous dynamic behavior of the bearing and gear centers under varying operational conditions emphasizes the need for careful selection of parameters such as damping ratio and unbalance to avoid chaotic motions. These results provide valuable insights into the design and optimization of gear-bearing systems, ensuring reliability and extending service life.