Modeling Interactions Between Flexible Flapping Wing Spars, Mechanisms, and Drive Motors

A system of dynamical equations is presented that allow micro air vehicle (MAV) ornithopter designers to match drive motors to loads produced by flexible flapping wing spars. The model can be used to examine the coupled system-level behavior of brushed DC motors, gear trains, and any number of linkages and flexible wing spars. A Lagrangian approach is used to derive the governing differential equations of motion for a class of ornithopter drive systems. Methods used to determine parametric constants contributing to generalized force components, which cannot be derived from first principles, are described. An example is presented where simulation results are compared to experimental measurements. The results show that the differential equations correctly predict major trends in observed motor speed and wing spar structural deformation over the course of each wingbeat. The results show that when pairing flight-weight motors and wings, significant variations in drive motor speed occur throughout each wingbeat. It is shown that coupling between motor speed, wing loads, and structural flexibility cause the aerodynamic forces encountered by the wing spars to depart from those predicted by rigid-spar and constant-velocity-motor-based kinematic simulations.