Investigation of Jump Resonance of a Horizontal Axis Washing Machine for Nonlinear Vibration using the Harmonic Balance Method

Abstract

In this work, a drum-type horizontal axis washing machine with two springs and two dampers has been considered to study the jump resonance phenomenon. Here two springs and two dampers are used and effects of nonlinear spring stiffness on vibration level in both horizontal and vertical directions have been investigated. In this study, a mathematical model of a horizontal axis washing machine is formed. A separate analysis is carried out in both vertical and horizontal directions by considering the whole system as a two degree of freedom system. As vibration magnitude is large due to unbalance mass of wet clothes, hence nonlinear stiffness of spring is considered. The analytical solution for the mathematical model is found using the harmonic balance method. One term expansion is used in this method to study the response of the system. To study the vibration response of the system, one term expansion is used. From this study, it has been found that the spring with cubic nonlinear stiffness increases the amplitude of vibration. Also, with the increase in cubic non-linear stiffness, the system tends to have multiple equilibrium positions. These equilibrium positions may be stable or unstable. It has been detected that the vibration amplitude has three different values for a few excitation frequencies due to cubic stiffness. So, the response of the system suddenly increases and then decreases due to cubic non-linearity which indicates the jump resonance.