Dynamic Analysis of Wind Turbine Planetary Gears Using an Extended Harmonic Balance Approach: Preprint

The dynamics of wind turbine planetary gears with gravity effects are investigated using an extended harmonic balance method that includes simultaneous internal and external excitations. This method along with arc-length continuation and Floquet theory is applied to a lumped-parameter planetary gear model including gravity, fluctuating mesh stiffness, bearing clearance, and nonlinear tooth contact to obtain the planetary gear dynamic response. The calculated responses compare well with time-domain-integrated mathematical models and experimental results. Gravity is a fundamental vibration source in wind turbine planetary gears and plays an important role in system dynamics, causing hardening effects induced by tooth wedging and bearing-raceway contacts. Bearing clearance significantly reduces the lowest resonant frequencies of translational modes. Gravity and bearing clearance together lower the speed at which tooth wedging occurs below the resonant frequency. Nomenclature b Backlash f, F Force vector i Harmonic number I Inertia k Support stiffness L Characteristic length M Characteristic mass N Number of planets m,n,p,q Sidebands r Base radius R Number of harmonics u Rotational displacement x, y Translations of the carrier, ring, and sun x, z System degrees of freedom β Helix angle ∆ Bearing clearance η, ξ Translations of the planets wrt carrier θ Rotational displacement τ Time ω Characteristic frequency Ω1, Ω2 Excitation frequencies ψ Pressure angle Subscripts B Bearing c Carrier m Mesh p Planet r Ring s Sun 1, 2...N Planet number Superscripts b Back-side d Drive-side