Mathematical Modeling of Flapping Wing Movements When Interacting With a Resisting Medium

Abstract

The work objective. The paper deals with the issues of modeling biologically inspired movement of an unmanned flying platform (UFP) equipped with flapping wings. Special attention is paid to modeling the interaction of a flapping wing with a resisting air medium. Therefore, the study aim is mathematical modeling of the force which occurs when the wings interact with the resisting medium.
 The problem to which the paper is devoted. To solve the problem is to make the mathematical model of the rotational motion of drone wing taking into account kinematic and dynamic features of two-coordinate rotation for various angle changing relative to the longitudinal and transverse axes.
 Research methods. Methods of classical mechanics, theory of motion stability, optimal control, observations, parametric optimization were used to solve the problem.
 The novelty of the work lies in the algorithms for changing the angles of wings rotation relative to the longitudinal and transverse axes, presented as smooth functions. A method for defining the reduced force arising during the wing movement is proposed. The dependences of the reduced force of wing-air interaction are obtained which provide the development of lifting and traction forces. These forces allow the drone to move in space along a given trajectory.
 The study results. The modes of flapping wing motion are simulated and the dependences of instantaneous force values which the wing creates during movement are obtained. These forces allow the drone to move in space along a given trajectory. It is shown that the drone movement is controlled by changing the frequency and amplitude of the wing vibrations, as well as by changing the angle of theneutral line inclination relative to which the wing rotates.
 Conclusions: a model of the reduced force arising from the flapping wing movement is proposed. Dependence graphs of the effective wing area (frontal area) for various parameters of changing rotation angles from time are constructed. Flapping wing motions of the aircraft is simulated. The range of parameters is defined at which the wing movement projections create horizontal F1x and lifting F1z forces at different values of area projections S1x, S1y, S1z.