The limits of the beam sag under influence of static magnetic and electric force
Utilization of a magnetic force can be found in many mechatronic applications, where e.g. a slender beam or plate is subjected to static magnetic force generated by an electromagnetic actuator consisting of a solenoid wound on a ferromagnetic core and a ferromagnetic armature, fixed to the beam. The static magnetic force, acting perpendicularly onto the beam, causes sag (downwards bending) of the beam. If the magnitude of the magnetic force surpasses some threshold value the armature and hence the beam is completely attracted to the core of the solenoid. For small deflections the mathematical expression of the magnetic force can be linearised and approximated by a polynomial dependence on the distance to the electromagnet. In practical applications, it is important to analyse the nature of the sag and to determine the limits of the linear approximation, as well as the limits leading to the full attraction to the electromagnet. The mathematical generalisation of the sag is valid for electrostatic force between planar electrodes, too.