Free spatial vibrations of axial fan

Abstract

This work presents a mechanic-mathematical modelling of the free undamped spatial vibrations of an axial fan. The kinematics of this mechanical system is studied. The considered mechanical system is consisted of three rigid bodies and it has 18 degrees of freedom. The transformation matrix from the local coordinate systems to the reference coordinate system is defined. The vectors of the position and the vectors of the linear velocities of random points of the bodies are deduced. The vectors of the angular velocities of the bodies, projected in the local coordinate systems, are defined. Results from the kinematics study are used for investigation of the dynamics and vibrations of this mechanical system. The kinetic energy and the potential energy of the system are determined. The differential equations of free vibrations are deduced. They take into account the mass, (the) elastic and geometric proper- ties of this mechanical system. Some purposeful calculations are performed for a fan with concrete parameters. The natural frequencies and the mode shapes are determined and illustrated during small vibrations of this fan.