Dynamic response analysis on torsional vibrations of wind turbine geared transmission system with uncertainty

Gearbox transmission system is the major part of the wind turbine drive train. Due to the manufacturing and assembling errors, lubrication condition, wear and uncertainties in material and geometric properties, the system parameters, including mesh stiffness, transmission error and damping of the meshing gears are always uncertain. For a more reasonable evaluation of dynamic characteristics of the gearbox transmission system, the influence of the uncertain parameters should be taken into consideration. Based on the Chebyshev interval method (CIM), the dynamic responses of a geared transmission system with uncertain parameters are thus investigated in this paper. A torsional vibration model is derived for a geared system, in which some parameters including the mesh stiffness, the transmission error, the mesh damping, the shaft damping, the moment of inertia of the input blades and the torsional stiffness of the driving coupling shaft are considered as uncertain but bounded parameters. Interval dynamic equations of the geared system are solved by use of the CIM in combination with the variable-step Runge-Kutta numerical integration method. The accuracy of the CIM is demonstrated in comparison with the Monte Carlo (MC) simulation. Variations of the upper and lower bounds of the dynamic mesh force with input speed are obtained. The effects of those uncertain parameters on the frequency response of the dynamic mesh force are discussed in detail. It is shown that small parameter uncertainties might be propagated in the vibration system and lead to relatively large uncertainties of the dynamic response of system. The result is of significance for the design and condition monitoring of wind turbine drive trains.