Two parametric excited nonlinear systems due to electromechanical coupling

This paper analyzes the behavior of two electromechanical systems. In the first part of the work, a simple system is analyzed. It is composed of a cart, whose motion is excited by a DC motor (motor with continuous current). The coupling between the motor and the cart is made by a mechanism called scotch yoke, so that the motor rotational motion is transformed in horizontal cart motion over a rail. The developed model of the system takes into account the influence of the DC motor in the dynamic behavior of the system. It is formulated as an initial value problem, in which the coupling torque between the mechanical and electric systems appears as a parametric excitation. By simulations, it is verified that the system has a periodic solution with a relation 2:1 between the period of rotation of the disk (part of the electromechanical system) and the period of the current in the DC motor. In the second part of the work, a pendulum is embarked into the cart. Its suspension point is fixed in cart, so that there exists a relative motion between the cart and the pendulum. The excitation of the pendulum comes from the motion of the cart, so it is not controlled and can vary widely because the pendulum can store energy. The pendulum acts as a hidden parameter of the system. The influence of the embarked pendulum in the dynamic behavior of the system is investigated and it is shown how it can affect the solutions of the dynamic equations.