Uncertainty Quantification of the Nonlinear Dynamics of Electromechanical Coupled Systems

Abstract

Abstract. This paper analyzes the nonlinear stochastic dynamics of electromechanical systems with friction in the coupling mechanism and in the mechanical parts. Two different electromechanical systems were studied. The first one is composed by a cart whose motion is excited by a DC motor and in the second a new element,a pendulum, is attached to the cart. The suspension point of the pendulum is fixed in cart, so that exists a relative motion between them. The influence of the DC motor in the dynamic behavior of the system is considered. 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. In the model of the system, it is considered the existence of friction in the coupling mechanism and in between the cart and the rail. The embarked pendulum is modeled as a mathematical pendulum (bar without mass and particle of mass m p at the end). The embarked mass introduces a new feature in the system since the motion of the pendulum acts as a reservoir of energy, i.e. energy from the electrical system is pumped to the pendulum and stored in the pendulum motion, changing the characteristics of the mechanical system. Due to the consideration of friction, the dynamic of the problem is described by a system of differential algebraic equations. One of the most important parameters of the problem is the amplitude of the cart motion that is given by the position of the pin used in the coupling mechanism. The behavior of the system is very sensitive to this parameter because it controls the nonlinearities of the problem. In the stochastic analysis, this parameter is considered uncertain and is modeled as a random variable. The Maximum Entropy Principle is used to construct its probability model. Monte Carlo simulations are employed to compute the mean motion and the 90% confidence interval of the displacements of the pendulum, of the cart and of the angular speed of the motor shaft.2026