Study on steady-state response of a vertical axis automatic washing machine with a hydraulic balancer using a new approach and a method for getting a smaller deflection angle

Abstract

A new approach is used in this paper to analyze steady-state response of a vertical axis automatic washing machine with a hydraulic balancer and a method for getting a smaller deflection angle of the washing/drying assembly is presented. First, a mathematical model of the vertical axis washing machine and a numerical description of the hydraulic balancer are described and a vibration model for the vertical axis washing machine with a hydraulic balancer is built. Second, the vibration model is transformed into an autonomous form whose equilibrium point can be used to analyze dynamics of the washing machine at the steady state. Because the autonomous form can be solved by the Newton–Raphson method which requires only a few iterations, it provides a much faster approach for analyzing steady-state response of the spin drying process than traditional numerical integration methods. Five parameters influencing the spin drying process are considered, and the balancer's importance in reducing vibrations at the steady state is illustrated. Third, the equilibrium conditions of the centrifugal forces acting on the clothes, the washing/drying assembly and the balancer are considered, and a governing equation for getting a smaller deflection angle of the washing/drying assembly is derived. At last, parameters in the governing equation, especially those related to the hydraulic balancer, are discussed.