Planetary gearboxes generate considerable noise and vibration due to high bearing loads and nonlinear dynamic behaviors. Excessive vibration leads to gear tooth and bearing failures. Despite of archival gearbox research, there are a few research aspects that are not fully-developed. They are: 1) tooth wedging (tight tooth mesh) and its connection with planet bearing failures; 2) nonlinear dynamics of planetary gears with bearing clearance; 3) stiffness determination of rolling element bearings; and 4) multi-body gearbox modeling linking gearbox vibration and noise radiation.
Analyzing dynamic bearing and tooth loads of planetary gears is essential to improve gearbox reliability. Chapter 2 focuses on tooth wedging in wind turbine drivetrains, which is a potential source for gearbox failures. Lumped-parameter and finite element/contact mechanics models of planetary gears with tooth wedging, gravity, aerodynamic excitations, and mesh stiffness variation are developed to compute dynamic bearing or tooth forces. Tooth wedging elevates planet bearing forces and disrupts load sharing. A method to quantify tooth wedging is developed and verified.
Bearing clearance in planetary gears introduces nonlinear behaviors and bifurcations, which have not been investigated in the past. In Chapter 3, numerical integration and harmonic balance are applied to the analytical model, while Newmark method is used for the finite element model. Floquet theory determines solution stability. Complicated nonlinear effects, coexisting solutions, bifurcations, and chaos are exhibited in the dynamic response. Input torque can potentially eliminate some of the nonlinear effects caused by bearing clearance.
Bearings are critical components in drivetrains. Accurate modeling of rolling element bearings is essential to assess vibration and noise of drivetrain systems. In Chapter 4, a full fidelity finite element model of rolling element bearings is developed. A combined surface integral and finite element algorithm is used to analyze the rolling element contact. A numerical method based on finite difference formulation is developed to determine the full bearing stiffness matrix. This method is validated against experiments. Techniques that reduce computational effort and improve result accuracy are discussed.
Vibration and noise caused by gear dynamics at the meshing teeth propagate through power transmission components to the surrounding environment. Chapter 5 is devoted to developing computational tools to investigate the vibro-acoustic propagation of gear dynamics through a gearbox using different bearings. Detailed finite element/contact mechanics and boundary element models of the gear/bearing/housing system are established to compute the system vibration and noise propagation. Both vibration and acoustic models are validated by experiments including the vibration modal testing and sound field measurements. The effectiveness of each bearing type to disrupt vibration propagation is speed-dependent. Housing plays an important role in noise radiation. It, however, has limited effects on gear dynamics.