Stability and dynamic analyses of a horizontal axis washing machine with a ball balancer

•Mathematical model of a horizontal axis washer with a ball balancer is built.•Stability analysis considering the influence of gravity is carried out.•Cone shape trajectory of the tub's axis is observed.•Backward mass center design of the tub assembly can reduce vibration angle.

A mathematical model of a horizontal axis washing machine with a ball balancer is built. The Floquet multipliers are employed for judging the stability of the system based on which a special continuation program considering the influence of gravity is developed. Stability analysis is carried out with stable and unstable regions above 4 Hz discovered. Influences of several parameters on variations of the boundaries between the regions are discussed. Dynamics of the spinning cycle in Stable region 1 are studied. The phenomenon that the tub's axis moves along the lateral surface of a cone is discovered based on which equilibrium of the centrifugal forces is discussed and a potential method for getting a smaller vibration angle is proposed. A ball balancer is produced for experiment with its lubrication and defects due to friction discussed. Quantitative experiment is done on a commercial washing machine with instability of the balancer, the cone shape trajectory of the tub's axis and the method of obtaining a smaller vibration angle validated.