Dynamics of Vibratory Bowl Feeders

In this work we construct a simple dynamical model for vibratory bowl feeders. The symmetrical arrangement of the springs supporting the bowl allow us to predict a simple structure for the stiffness matrix of the system. The cylindrical symmetry of the bowl itself then means that the linearized rigid body dynamics of the system can be simplified to a 2-dimensional system. The solutions to this system are elliptical motions of the bowl, vibrating about the symmetry axis and along it at the same time. We are able to find a condition for the system to be at resonance. There is some debate about how the parts move up the helical track inside the bowl. We are able to show that one alternative, a “slip-stick” motion, is unlikely.