4 - Mechanical dynamics

Abstract

This chapter describes the dynamic characteristics of a simple mechanical system. A two-axis system consists of a shaft rotating at an angular speed of ωrm around the k-axis. The three perpendicular x-, y-, and z-axes are in the stationary coordinate reference frame. The other three perpendicular i-, j-, and k-axes are in the rotational coordinate reference frame. The bottom of the shaft is fixed to the origin of these axes. A cylindrical magnetic bearing rotor is fixed to the shaft at a length lrt from the origin. The k- and z-axes are almost aligned under normal conditions. The k-axis is inclined by an angular position θy from the z-axis. A moment (or torque) Ny is applied around the y-axis. The chapter also discusses a five-axis active suspension system. There are two radial magnetic bearings and one thrust magnetic bearing. The first radial magnetic bearing generates radial forces in x1- and y1-axis directions. The second radial magnetic bearing generates radial forces in x2- and y2-axis directions. A thrust magnetic bearing generates a z-axis suspension force. The radial shaft movements can be expressed by translational and inclination movements.