Rigid-flexible coupled dynamic modeling and torque-component decomposition of a 5R parallel mechanism for wind turbine blade fatigue testing via Kane’s method

Full-scale fatigue testing is essential for ensuring the structural reliability of large wind turbine blades, and biaxial fatigue testing methods can not only better reproduce the loads experienced by blades but also reduce the testing time; therefore, biaxial fatigue testing equipment has attracted increasing attention. However, existing biaxial fatigue testing equipment based on a floor-mounted 2-DOF 5R parallel mechanism still faces significant dynamic modeling challenges under the coupled condition of a rigid driving mechanism and a highly compliant nonlinear load. In this study, Kane’s method is employed not as a new dynamic algorithm but as an efficient formulation tool to establish a problem-specific rigid–flexible coupled model of the mechanism interacting with a compliant nonlinear blade. The model incorporates mechanism inertia and the blade’s stiffness and damping. Through partial velocity projection, the nonlinear viscoelastic blade reaction is mapped from Cartesian space into the generalized active forces, avoiding explicit calculation of internal constraint forces. The driving torque is decomposed into inertial, gravitational, and blade-flexible-load components to identify the dominant torque source under low-frequency, large-displacement loading. Kinematic and dynamic simulations are conducted in MATLAB/Simulink, and the model is numerically verified against an MSC ADAMS virtual prototype. The predicted driving torques show good numerical consistency, with a root-mean-square error below 1.5% and a maximum relative error below 3.5% under representative conditions. The torque-component decomposition further indicates that, under a low-frequency and large-displacement condition of 0.5 Hz, the driving torque is dominated by the elastic load of the blade, which contributes more than 80% of the total torque, whereas the inertial contribution remains comparatively small. The proposed model can provide a theoretical and numerical basis for dynamic analysis, motor sizing and feedforward control design of biaxial fatigue testing equipment for wind turbine blades.