Stability analyses of a vertical axis automatic washing machine without balancer

This paper analyzes the nonlinear vibration characteristics associated with the spin drying process of a vertical axis automatic washing machine without any balancer. At first, damping properties born with the machineʹs suspension system are discussed and a mathematical model involving tangential damping forces is built. Based on a rotating coordinate transformation, this model is then converted to an autonomous form for stability analyses. The continuation and bifurcation software AUTO [1] is applied and a Hopf bifurcation phenomenon is observed from a one-parameter bifurcation diagram. Based on several two-parameter bifurcation diagrams, several parameters affecting the Hopf bifurcation are then discussed. At last, bifurcation results are validated by time responses of the autonomous system. For a further view of the spin drying process, simulations of the non-autonomous system are also provided. This paper provides a new insight into the spin drying process of the vertical axis automatic washing machine.