Modeling and analysis of vibratory feeder system based on robust stick-slip motion

This study presents model and analysis of a robust one-dimensional stick-slip transportation of an object, on dry contact with an oscillating platform suspended by nonlinear leaf spring. The oscillating platform is designed and modeled such that the elastic spring constant is direction dependent. A recursive analytical solution algorithm is proposed to solve nonlinear system dynamics. The system and the input force parameters are both investigated with goal to optimize the average velocity of the object. Both experimental and analytical results showed that the stick-slip motion is highly nonlinear and sensitive to the system and input force parameters. Moreover, the simulations showed that it is feasible to design a platform with robust sets of parameters (natural frequencies) and further use the input force parameters (amplitude and driving frequency) to tune for desired average velocity, under given dry friction conditions.